Last week, Puerto Rico raised the official death toll of Hurricane Maria to 2,975, making it the deadliest storm in at least 50 years.

But that number may also make history of a different sort—if, as expected, it includes a record number of indirect deaths.

“At the moment, the largest we have is Katrina with more than 500 indirect deaths,” said Ed Rappaport, a meteorologist with the National Hurricane Center who tracks storm-related fatalities. “I’d be surprised if that number was not exceeded greatly.”

Direct deaths happen when someone drowns in a storm surge or is killed when a building collapses or perishes in other circumstances caused by the physical forces of the storm.

Indirect deaths are less straightforward. They may occur days, weeks or months after a storm hits, or even before it makes landfall. The primary cause might be a heart attack, a gap in medication, a fall from a ladder or some other event that doesn’t overtly appear weather-related.

“If you looked at media reports, prior to the 1980s, there are few with any explicit references to indirect deaths,” Dr. Rappaport said. “The focus was on the loss due to storm surge” and other direct causes.

Because of improved storm forecasts and disaster preparation in recent years, the number of direct deaths has, on average, trended down, focusing attention on indirect deaths, which, proportionately, have become increasingly prevalent.

“By way of example, the 1900 hurricane in Galveston, Texas, killed 8,000 to 12,000 people, and the 1928 Lake Okeechobee hurricane caused 2,500 to 3,000 fatalities,” Dr. Rappaport said. “Those, we believe, are almost entirely totals of direct deaths.”

In contrast, Hurricane Katrina—until Maria, the deadliest storm in recent years—caused 520 direct deaths and 565 indirect deaths. Another 300 or so couldn’t be categorized, according Dr. Rappaport’s research.

Failing to account for indirect deaths could cause the scale of a storm to be underestimated which, in turn, could undermine the emergency response or impair future disaster planning. But counting them is difficult.

“There are gray areas,” Dr. Rappaport said. “There are judgment calls.”

The most basic tool for tallying up disaster-related fatalities is the death certificate. However, in Puerto Rico, perhaps due to a lack of training, few of these documents flagged Hurricane Maria as a cause of death.

Initially, only 64 Puerto Rican fatalities were attributed to the storm, despite an overall spike in deaths following Maria’s landfall on Sept. 20.

“The demographic registry knows their daily and monthly average,” said Ann Goldman-Hawes, an epidemiologist at George Washington University who, with a team of independent researchers, arrived at the now-official death toll. “They can see that if they normally have 75 deaths a day, and they have 120 coming in, you have excess deaths.”

The information contained in the certificates was accurate, the researchers found, but when it came to recording the role of the hurricane, it was incomplete.

To arrive at their estimate, Dr. Goldman-Hawes’s team examined how many deaths normally occurred each month in Puerto Rico in the seven years before the hurricane versus how many occurred in the aftermath of the storm.

“You can look at the deaths you would have expected and then look at how many deaths there actually were,” Dr. Goldman-Hawes said. “Then you can make an estimate.”

But this approach answers only one question: How many people likely died because of the hurricane? It doesn’t distinguish between direct and indirect deaths, nor does it provide information about the causes.

“The question is where are people dying and what are they dying of,” Dr. Goldman-Hawes said.

Dr. Goldman-Hawes and her team would like to continue the research in hopes of pinning down these details, which could involve examining death certificates and interviewing survivors, but in the absence of funding, questions like these may never be answered.

Meanwhile, the Centers for Disease Control and Prevention provides guidance for filling out death certificates following a disaster.

“It’s written to explicitly address this, that the coroner or medical examiner isn’t writing down the death is related to the disaster,” said Margaret Warner, an epidemiologist with the CDC’s National Center for Health Statistics, referring to the latest publication explaining the guidelines. “Unfortunately, it wasn’t out on street long enough ahead of time to percolate to Puerto Rico.”

Moving forward, the CDC and others hope the guidance will lead to better disaster-related death tallies.

“The last service a doctor does for a patient who dies is fill out a death certificate,” Dr. Goldman-Hawes said, “It has to be done the right way to serve the family and the community.”

Write to Jo Craven McGinty at Jo.McGinty@wsj.com