Investigators on Tuesday were focusing on whether a gunman had been targeting the headquarters of the National Football League when he burst into an office tower in Midtown Manhattan and killed four people, including a police officer, in a rare episode of deadly mass violence in the city.

Mayor Eric Adams said on Tuesday morning that the authorities “have reason to believe that he was focused on the N.F.L.,” which has offices at the tower, 345 Park Avenue. A three-page note found on the gunman mentioned the league, as well as claims that the man had suffered from the degenerative brain disease chronic traumatic encephalopathy, or C.T.E., from playing football, the police said. It asks that his brain be examined for signs of C.T.E. and accuses the league of concealing the dangers of the game.

Mr. Tamura shot himself in the chest, rather than the head.

“Study my brain please,” the note said. “I’m sorry.”