Ballistics tests on Smith's weapon showed an apparent match to a bullet recovered from Chasen's body, the source says.
Chasen, 64, was shot multiple times in Beverly Hills while driving her Mercedes-Benz in the early morning hours of Nov. 16 after leaving a party for the Burlesque premiere.
Investigators believe a vehicle pulled up next to her car while she was stopped at a red light and an assailant fired shots through her passenger-side window, according to a coroner's document obtained by Los Angeles station KTTV.
Smith, 43, a transient with a long rap sheet of robbery and drug crimes, shot himself in the lobby of a Hollywood apartment building Dec. 1 after Beverly Hills detectives approached him for questioning.
According to Smith's neighbor, Terri Gilpin, 46, Smith had openly bragged in the days following Chasen's death that he was the killer, but questions were raised about whether Smith was telling the truth.
"He said, 'You know that publicist they're talking about on TV? Yeah, I killed her. I'm getting $10,000 for killing her. I did it, I did it,'" Gilpin said.
"He'd often brag that he had a gun and would kill anyone who got in his way," Gilpin added. "He told my husband he'd been to prison twice and that he'd rather die than go back."