Lee Dell Thomas Jr., 44, of Dallas, fell to his death early Tuesday, about 14 hours after he climbed into the crane towering over the Southern Methodist University campus in suburban Dallas.
"It was an unfortunate outcome," Assistant Chief Thomas Lawrence said at a news conference. "But we have to resolve things the best way we can. We tried to do the best we could."
Thomas' mother told a local television station Tuesday that she wasn't surprised to learn of her son's death and that their family had a history of mental illness.
Police said Thomas claimed he was armed and threatened to shoot anyone who approached him. Lawrence said no weapon was found on Thomas or in the crane cab.
Thomas also had covered the area around the cab with grease to prevent officers from reaching him.
Lawrence said that Thomas was "a person of interest" in the hijacking early Monday of a truck containing band equipment, but he hadn't been conclusively linked to the heist.
Online criminal records showed that Thomas spent 13 years in the Texas state prison system for a 1991 aggravated assault conviction and a subsequent conviction for aggravated assault while in prison. He was released in 2004.
Ollie Mae Thomas told KTVT-TV of Fort Worth and Dallas on Tuesday that her son - and her family - had a history of mental illness. Lee Dell Thomas' grandfather committed suicide and his father was a paranoid schizophrenic, she said. She also said her son began using drugs at an early age.
She said Lee Dell Thomas sought treatment for his mental illness when he left prison, but quit taking the medication after two months.
"He said he didn't like the way the medication made him feel," Thomas said.
Thomas' mother told the television station that her son worked odd jobs and sometimes lived with her.
Friday night, though, she said he looked and seemed different.
"In his eyes, it didn't look like he cared about nothing at all," Thomas told the station.