Methods for counting storm deaths vary by state and locality. In some places, officials include only direct deaths, such as people who drown in storm floodwaters. Puerto Rico’s method is not that restrictive; the medical examiner includes some deaths indirectly caused by a storm, such as suicides.

The leading causes of death on the island in September were diabetes and Alzheimer’s disease, Puerto Rican government data show. But there was a sharp spike — by 50 percent — in the number of recorded deaths from sepsis, a complication of severe infection that can be tied to delayed medical care or poor living conditions.

Reviewing the circumstances surrounding each death will require interviewing family members and doctors who signed death certificates to find out if, for example, a heart attack might have been brought on by stress from the hurricane, or might have been fatal because an ambulance could not get through debris-blocked streets in time to help.

Harry Figueroa, a 58-year-old teacher, died in Caguas on Oct. 4 from pneumonia, and his family blamed the power outage for his death. His daughter, Lisandra M. Figueroa, said her father was obese and needed the help of a CPAP machine to keep breathing safely while asleep, but it would not work without power.

“Between the dust, the rain and the heat, he kept getting sicker,” said Ms. Figueroa, 30.

She was skeptical that the government could adequately investigate all of the cases like his on the island.

“I don’t know if it will be possible, because of the chaos in this country,” she said. “I don’t know how they’re going to do that. They’re going to have to request autopsies of all the bodies.”