(CNN) Deaths across America spiked as Covid-19 began its spread, and many were never attributed to the new coronavirus, researchers reported Monday.

"Notable increases" in deaths were seen in March and early April, the team led by the Yale School of Public Health found. This was especially true in New York and New Jersey, states hard-hit by the pandemic.

The study was first reported by the Washington Post.

Using data from the Centers for Disease Control and Prevention, the team found about 15,000 excess deaths from March 1 to April 4. During the same time, states reported 8,000 deaths from Covid-19. "That is close to double," Dan Weinberger, who studies the epidemiology of infectious diseases at Yale, told CNN.

The team could not show whether the increased deaths were due to coronavirus, Weinberger said. But there are strong indications that they were. For instance, the team also looked at data on doctor visits.

"What we see is that in many states, you see an increase in influenza-like illnesses, and then a week or two later, you see an increase in deaths due to pneumonia and influenza," Weinberger said. "It provides some confirmation that what we are seeing is related to coronavirus."

Plus, in especially hard-hit states such as New York and New Jersey, where coronavirus is known to have spread widely and infected many people, overall deaths were far in excess in what would normally have been expected in March.

"In New York City, this discrepancy was even more stark, with three to four times as many excess all-cause deaths as pneumonia and influenza deaths," the team wrote.

Some states, such as New York, seemed to keep up with the Covid-19 deaths. The state reporting of deaths in the pandemic closely tracked what the Yale team found. But others did not.

"For instance, California had 101 reported deaths due to COVID-19 and 399 excess pneumonia and influenza deaths," the team wrote in a preprint published online in MedRxiv (pronounced Med Archive).

The new coronavirus causes respiratory disease, and deaths would presumably be listed among the regular reports of deaths and illness from pneumonia and influenza. But doctors are increasingly reporting other, sometimes fatal, symptoms from Covid-19, including strokes, kidney failure and heart damage.

Patients already weakened by pre-existing conditions such as diabetes, cancer and heart disease may have had a death listed as being due to one of those causes, rather than coronavirus.

Plus, it's possible that coronavirus lockdowns would have led to a lower-than-average death rate. For instance, if fewer people were driving, traffic deaths could be expected to fall, Weinberger said.

So Weinberger's team looked at both deaths from pneumonia and influenza, and deaths from all causes.

"We decided to look at all deaths from pneumonia, or all deaths overall, and see how those numbers were changing," Weinberger said.

The CDC tracks deaths from pneumonia and influenza by the week, and compares them to a baseline of deaths to keep tabs on the annual epidemic of seasonal flu. Separately, the National Center for Health Statistics, part of the CDC, keeps data on all reported deaths.

The Yale-led team subtracted the expected number of deaths for each week from the total number of deaths that were actually reported, and counted the extra as Covid deaths.

"Many states experienced a notable increase in the proportion of total deaths due to P&I (pneumonia and influenza) starting in mid-March through March 28 compared to what would be expected based on the time of year and influenza activity," the team wrote in their report.

Weinberger's team found evidence that people were dying as states struggled to find out if the virus had even arrived in their regions. "In some states, such as Florida and Georgia, the increase in deaths due to pneumonia and influenza preceded the widespread adoption of testing for the novel coronavirus by several weeks," they wrote.

The researchers said their work shows it may be more accurate to estimate Covid deaths, rather than try to count each and every positive test.

"Given the lack of adequate testing and geographical variability in testing intensity, this type of monitoring provides key information on the severity of the epidemic in different geographic regions," they wrote.

"It also provides some indication of the degree to which viral testing is missing deaths associated with COVID-19 directly or indirectly."

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Some public health experts have said Covid-19 was almost certainly spreading in the United States in January and perhaps as early as December, long before the U.S. reported the first official death. Some state and local health officials are going back to see if people who died in January and February may have in fact been infected with coronavirus.