The Utah man accused of shooting an off-duty Los Angeles County sheriff's deputy Monday and killing another man an hour earlier had told his family he wanted to "make it on his own or die," police said Wednesday.

The family of Rhett Nelson, 30, contacted St. George police on May 27 and said he'd left their Utah home "without any specific reason" with a gun but they did not think he was suicidal or a danger to anyone else, Capt. Mike Giles said.

"He made a statement to them or somehow communicated he wanted to make it on his own or die," Giles said. They formally reported him missing the next day and said they believed the gun was for self-defense. It was not immediately known who owned the weapon.

Police say Nelson shot Deputy Joseph Gilbert Solano in the head Monday at a Jack in the Box restaurant in the eastern Los Angeles suburb of Alhambra after fatally shooting a 30-year-old man in downtown LA in attacks that both appear to be random. Solano remains in grave condition.

Nelson has a history of mental illness and a history of opiate abuse, though he had been clean for about six months, according to statements from his father, Bradley Nelson. The family is "devastated beyond words" by the attacks and is cooperating with authorities.

"We believe we made every effort to help Rhett and bring him home safely without harm to himself or others, but despite our best efforts we were unable to locate him before this horrific act," the statement said.

On June 4, Nelson called his family from Rancho Santa Margarita in Orange County, Giles said. They still believed he was safe and police removed him from a missing persons database the next day.

On Wednesday, the Los Angeles County Sheriff's Department released Nelson's booking photo as part of an effort to seek any additional victims. Homicide investigators believe he may have been involved in other crimes in California.

Giles said no recent crimes involving Nelson have been reported to St. George police.

The Salt Lake Tribune reported that Nelson didn't have a violent criminal history in Utah but had previously pleaded guilty to driving with a "measurable amount" of a controlled substance in his body and guilty to underage alcohol offenses.

Los Angeles authorities recovered a gun from Nelson's car. It was not immediately clear if it was the firearm from Utah.