The U.S. gunman who lured two firefighters to their deaths died of a self-inflicted shot to the head and wasn't hit by return fire from a police officer, New York State Police said Thursday.

Investigators still hadn't made a positive identification of the body found in 62-year-old William Spengler's burned house. They have said they believe the remains are those of his 67-year-old sister, Cheryl Spengler, who also lived there.

Spengler set his home and a car on fire before dawn on Christmas Eve, took up a sniper's position and opened fire on the first firefighters to arrive, authorities said. He wounded two firefighters and a police officer.

Autopsies showed that volunteer firefighter Michael Chiapperini died of a single gunshot and Tomasz Kaczowka was killed by two, police said.

Trooper Mark O'Donnell said investigators weren't releasing information about how Spengler got the military-style Bushmaster .223-calibre semiautomatic rifle, 12-gauge shotgun and .38-calibre revolver found with his body. He said they're still tracing the history of the guns.

Spengler spent 17 years in prison for killing his grandmother with a hammer in 1980 and was barred from possessing weapons as a convicted felon. Authorities said they had no encounters with him after he was released from prison.

After Monday's attack, investigators found a typed letter laying out Spengler's intention to destroy his neighbourhood and "do what I like doing best, killing people."

The Spengler siblings had lived in the home with their mother, Arline Spengler, who died in October. In all, seven houses were destroyed by the flames Monday.

Police Chief Gerald Pickering said police may never know Spengler's motive.

The wounded firefighters, Joseph Hofstetter and Theodore Scardino, were upgraded Wednesday to satisfactory condition.

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