NASHVILLE, Tenn. (AP) — Shot twice in the head and two more times in the chest, former NFL quarterback Steve McNair was the victim of a homicide, police declared Sunday. But authorities wouldn’t say it was a murder-suicide — even with his 20-year-old girlfriend dead at his feet from a single bullet.

McNair had been dating Sahel Kazemi for several months, and Nashville police spokesman Don Aaron said Sunday that a semiautomatic pistol was found under her body. She was shot in the head.

McNair, who was married with four sons, had a permit to carry a handgun in Tennessee, and he was arrested once before with a 9mm weapon although charges in the case were dropped. Police said they had not yet determined who owned the gun found at the scene.

Investigators weren’t looking for a suspect but were questioning friends of the couple as well as Kazemi’s ex-boyfriend. They were also waiting for results of drug and other laboratory tests before deciding whether McNair was killed in a lovers’ quarrel.

‘‘That’s a very important part of the investigation as we work to ultimately classify Miss Kazemi’s death,’’ Aaron said.

The details surfacing after McNair’s death stand in stark contrast to the public persona he enjoyed during his career.

McNair repeatedly played through serious injuries and pain to win, though he came up a yard short of forcing overtime in the Tennessee Titans’ famous drive in the 2000 Super Bowl.

Generous, he frequently took part in charity work for both the Titans and later the Baltimore Ravens after a 2006 trade. McNair even helped load donated food, water and clothes onto tractor-trailers that he had arranged for Hurricane Katrina victims, and paid for three football camps for children himself this year.

McNair and Kazemi were found dead at a Nashville condominium — which overlooks the Titans stadium — that he rented with his friend Wayne Neeley. Police believe both died early Saturday. Neeley found the bodies hours later, and called a friend, Robert Gaddy, who played at Alcorn State with McNair. Gaddy dialed 911.