Which deaths count toward the coronavirus toll? It depends on the state.

In Alabama, officials have ruled that one of every 10 people who died with COVID-19 did not die of COVID-19. Among those excluded from the numbers reported to the federal government were a bedbound patient with aspiration pneumonia in one lung and a person with a buildup of fluid and partial collapse of one lung.

Colorado, by contrast, has included some deaths in which the disease caused by the novel coronavirus was deemed probable — based on symptoms and possible exposure — but not confirmed through a test.

Health officials in both states say their approach is more accurate. Their divergent methods reflect a national debate over how to count the dead.

The U.S. government's COVID-19 death toll is widely believed to be an undercount because, at a time when access to testing has been severely limited, federal officials described their count as including only people who tested positive for the virus.

The Centers for Disease Control and Prevention updated its website this week to explicitly say that cases where the infection was not confirmed by a test may now be counted. But attributing a death to the virus can be a judgment call, experts say, and potentially a vexing one as indications emerge that the disease damages not just the lungs but also the heart, kidneys and other organs.

As a result, the overall tally — a benchmark broadcast constantly on cable news and elsewhere — is a less concrete figure than it appears. The inconsistent counting methods also raise questions about the ability to draw comparisons from state to state, and they play into a political debate about the reliability of the numbers.

» READ MORE: When death from coronavirus is a matter of interpretation

The scale of undercounting that may result from tallying only lab-confirmed cases was made clear Tuesday when New York City authorities began reporting the deaths of people who were suspected of having COVID-19 but never tested. The city's tally soared past 10,000 as the change added more than 3,700 fatalities.

"We are focused on ensuring that every New Yorker who died because of COVID-19 gets counted," Health Commissioner Oxiris Barbot said in a statement, adding, "While these data reflect the tragic impact that the virus has had on our city, they will also help us to determine the scale and scope of the epidemic and guide us in our decisions."

Since at least last month, Colorado has been reporting the deaths of people who were never tested but who showed symptoms and had close contact with an infected person. Three percent of Colorado's 329 deaths fall into this category of "epidemiologically linked" cases.

"They don't represent a large number of the deaths, but including them does give a more accurate number than excluding them would," said Ian Dickson, a spokesperson for Colorado's health department.

Asked how the national count is compiled, however, a CDC spokeswoman said on April 4 that the agency aggregates state tallies and counts only deaths in which the presence of the coronavirus was confirmed in a laboratory test, a method it acknowledged results in an "underestimation."

The next day, the Council of State and Territorial Epidemiologists, which represents state health officials, recommended reporting probable COVID-19 deaths, in addition to those with lab confirmations.

Ohio, Connecticut and Delaware have since begun reporting deaths of people who were presumed infected but had not been not tested. Ohio is reporting 361 deaths, 15 of which are listed as "probable" on the state's coronavirus data portal. Websites for the other two states do not disclose how many probable deaths are among their totals.

» FAQ: Your coronavirus questions, answered

On Tuesday, the day the CDC updated its website to say its tally now includes probable cases, agency spokeswoman Kristen Nordlund said three jurisdictions — she did not identify them — are reporting deaths of people who are believed to have died of the disease but were never tested.

The following day, a spokeswoman for Republican Gov. Larry Hogan announced Maryland would also begin counting probable deaths. By the afternoon, the state was reporting 349 deaths in lab-confirmed cases and 64 in probable cases.

Pennsylvania is also including deaths in probable cases, said Nate Wardle, press secretary for the state's health department. The state does not distinguish probable cases from confirmed cases in its public tally of deaths.

In Alabama, a physician reviews medical records of anyone who died and tested positive for the virus to determine whether a death should be attributed to COVID-19, according to Karen Landers, a spokeswoman for the state's public health agency.

Landers declined to provide information about the people who died with COVID-19 but were not counted in the state's official COVID-19 death toll. Those who had no respiratory symptoms could be excluded, she said, as could those who had an acute event such as a stroke or heart attack or who suffered trauma such as a car accident.

"Simply because persons have other medical diagnoses, they are not automatically excluded," she said. "Rather, other factors in the course of illness are taken into consideration on medical record review."

Asked about Alabama's method, Nordlund said the agency "reports the numbers the states provide to us."

As of Tuesday, a total of 110 people across Alabama had died and tested positive, but only 73 of them had been counted as COVID-19 deaths and reported to the CDC, according to state data published online. Twenty-five were still under review.

Twelve deaths — or one in seven of those where a determination had been made — were not attributed to COVID-19, Landers said. Those deaths are not reported to the CDC, and they are not included in the federal government's official tally.

Health officials in Jefferson County, which includes Birmingham, the state's largest city, said the 17 deaths of people who tested positive for the coronavirus had been reported to the county coroner's office. A physician conducting the health department's medical review found 11 deaths were attributable to COVID-19 and five were not. One was still under investigation.

The two patients who each died with problems in one lung were excluded because both lungs are affected in most cases of COVID-19, said Mark Wilson, who leads the Jefferson County Department of Health. Also excluded were two patients in hospice for other illnesses who were asymptomatic for the coronavirus, he said, and a person who died of sepsis and had other problems unrelated to COVID-19.

Wilson said he is concerned that Alabama is missing some deaths because of a lack of widespread testing. While other counties defer to the state in making these determinations, Jefferson alone conducts its own medical review of COVID-19 deaths.

Alabama's approach runs counter to the nationwide counting method described by Deborah Birx, a doctor and response coordinator for the White House coronavirus task force who has been one of most visible leaders of the federal response.

"In this country, we've taken a very liberal approach to mortality," she said at a briefing April 7, explaining that the United States is counting the deaths of people with underlying conditions as COVID-19 deaths, even though some other countries are not.

"The intent is, right now, that . . . if someone dies with COVID-19, we are counting that as a COVID-19 death," she said.

The CDC recently started using national data on respiratory illnesses, hospital visits and death certificates to better estimate coronavirus infections and deaths for a separate tally that it intends to begin reporting.

Health experts and elected officials use the official death count, along with the case count and other data points, to help assess the hardest-hit areas and determine the appropriate response. The tally has also become a politically charged statistic for a president who initially downplayed the pandemic and minimized its threat.

President Donald Trump has rejected concerns about an undercount, despite the CDC's acknowledgment. "The death counts, I think they're very, very accurate," he said last week in response to a reporter's question about limited access to testing.

Some of the president's defenders have pushed the theory — heavily promoted on Fox News and on conservative social media — that the nation's death toll is actually inflated because it includes the deaths of people who may have had COVID-19 but died of other causes.

In Alabama, Republican Gov. Kay Ivey was initially reluctant to order residents to stay home, saying she wanted to balance the state's public health and economic interests.

"I want to echo the president who today said, 'We have to get back to work,' " she said on March 24. "We must do everything we can to keep businesses open, and if they're closed, get them back up as soon as possible."

The following day, Ivey confirmed the state's first COVID-19 death.

Since April 2, the state website has included the number of deaths of people who have tested positive, along with the smaller number of people determined to have died from COVID-19 that is reported to the CDC.

"It's really just a matter of the accuracy of the data," Landers said. "It's an attempt to really look at this from a little more depth than just putting down, well, this person was positive for this and positive for that."

State Rep. Anthony Daniels, the Democratic leader in the Alabama House and a member of the state's coronavirus task force, said he was unaware of the state's approach to counting COVID-19 deaths until a Washington Post reporter contacted him about it last week. On Friday, he asked Alabama State Health Officer Scott Harris for a report detailing the number and causes of all deaths found not attributable to COVID-19. Harris declined an interview request for this story.

"I didn't know we were doing the process different than other states," Daniels said. "It's a fair question to ask: How are you making those decisions on attributed vs. reported?"

Jonathan Arden, a forensic pathologist who chairs the board of the National Association of Medical Examiners, said there can be a "gray zone'' when evaluating the death of a person who tested positive for the virus, showed COVID-19 symptoms and had an underlying condition like heart disease or suffered a heart attack. The virus could affect how much oxygen that person was receiving, he said.

"Can there be disagreement in how these things are concluded? Absolutely," he said. "You are talking about medical judgments, a diagnostic process that means you are arriving at an opinion."

Arden said Alabama's approach is valuable because including in the death tally everyone who had a positive coronavirus test "would be inflating the mortality rate." At the same time, he said, Colorado's approach is "valuable unless or until we have much more widespread testing. Otherwise there's a greater likelihood that we will miss cases we should have been capturing."

Marc Lipsitch, an epidemiologist at Harvard who has studied deaths from influenza, said he was concerned that Alabama may be filtering out deaths that were caused by the novel coronavirus, even if they didn't seem to be. Because contracting the flu can make patients more susceptible to a variety of problems, most deaths caused by the flu appear to have other immediate causes, such as heart attacks, stroke, cancer and diabetes.

"What Alabama is doing makes no sense," he said. "It's a well-established fact that respiratory viruses can cause a lot of their mortality through other causes. With something this new, saying if you don't see respiratory symptoms then you don't attribute it to COVID is overconfident at best."

Rachael Lee, a health-care epidemiologist at the University of Alabama at Birmingham hospital, said the state's approach is a sound way to try to get a more accurate count.

"We have the ability do that right now because we are not seeing as many deaths," she said. "I don't know how a state like New York could keep up with the process that we are doing."

Rendi Murphree, an epidemiologist at the Mobile County Health Department, said, "If we don't determine the cause of death, then we are potentially biasing the information."

Lina Evans, the coroner in Shelby County, said she was not notified that COVID-19 deaths would be reviewed before being counted. She said she began asking questions after she reported four deaths and noticed that none immediately appeared in the state death toll. Eventually, she said, they were all counted — but it took days and, in one case, a week and a half.

Evans said she worried that such delays have kept the count artificially low, contributing to a sense of complacency among Alabamians.

"They're still going to Walmart and social gatherings and continuing to push the peak out further. They don't take it seriously," she said.

State officials said the medical review is done expeditiously, often within a day, though the process can take longer if there is a lag in obtaining medical records.

Tyler Berryhill, the Madison County coroner, said he is more concerned about an undercount from limited testing than the possibility of an overcount. After one person with respiratory problems died in his county without getting tested for the coronavirus, he sent a sample to a state lab for postmortem testing.

"At rural hospitals and medical facilities, we know there was a shortage of testing," he said. "There's a big concern that we may not have total understanding of the true numbers in our state."

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The Washington Post’s Jacqueline Dupree and Lena H. Sun contributed to this report.