An emergency department physician in San Francisco recalled two deaths that were probably coronavirus but not identified as such. One patient died at home; a relative in the same home later tested positive for the disease. Another patient was an older man who came to the hospital with typical coronavirus symptoms, and who had been in contact with someone recently traveling to China, but arrived at the hospital before testing was available.

In New York City, emergency medical workers say that infection and death rates are probably far higher than reported. Given a record number of calls, many ambulance crews have encouraged anyone not critically ill to stay home. The result, medics say, is that many presumed coronavirus patients may never know for sure if they had the virus, so any who later die at home may never be categorized as having had it.

Across the country, coroners are going through a process of re-evaluation, reconsidering deaths that occurred before testing was widely available. Coroners and medical examiners generally investigate deaths that are considered unusual, or result from accidents or suicides, or occur at home.

Joani Shields, the coroner in Monroe County, Ind., said she wondered about a man diagnosed with pneumonia who died in early March.

A coronavirus test was requested at the time, but the local health department denied it, Ms. Shields said, on the ground that the supply of tests was too limited.

“I wish we could have tested him,” she said.

In Shelby County, Ala., Lina Evans, the coroner, said she was now suspicious of a surge in deaths in her county earlier this year, many of which involved severe pneumonia: “We had a lot of hospice deaths this year, and now it makes me go back and think, wow, did they have Covid? Did that accelerate their death?”

Ms. Evans, who is also a nurse, is frustrated that she will never know.

“When we go back to those deaths that occurred earlier this year, people who were negative for flu, now we’re having the ‘aha!’ moment,” she said. “They should have been tested for the coronavirus. As far as underreporting, I would say, definitely.”