Investigators have determined that Bryan Gonzalez, 12, died from a self-inflicted gunshot wound.
The death of Christian Gonzalez, 10, remains undetermined.
Investigators are awaiting additional results from forensic tests.
Investigators say there were no signs of other abuse.
The two bodies were found Tuesday by a family member behind their Chino Hills mobile home.
Authorities say their father's handgun was the weapon.
The gun was kept in an unlocked case.
Investigators say there were no suicide notes.
Interviews with family members and neighbors have not produced any kind of rationale for the double shooting.
Officials say the investigation will be forwarded to the district attorney's office for possible criminal action because the handgun was not secured.
The Associated Press contributed to this report.
