Anchorage Police said Thursday that a South Anchorage family found dead last week were killed in a murder-suicide.

"At this point in the investigation, all indications are that Curtis Young III shot and killed his girlfriend and their children before turning the gun on himself and taking his own life," police wrote in a release Thursday morning.

Young, 24; Desiree Leandra Gonzalez, 27; Zaiden E. Young, 4; and 17-month-old Zarielle A. Young were found dead in their South Anchorage apartment at the 500 block of East 74th Avenue on May 13.

Police quickly labeled the crime a "domestic violence-related incident" last week, but until Thursday hadn't said who they suspected of perpetrating it.

According to court records, police had previously responded to multiple domestic disturbances involving Curtis Young in 2010 and 2011. Young was jailed for putting Gonzalez in a chokehold until she passed out twice in 2011. The couple had been together for at least six years, a family member said.

In a press conference last week, Sgt. Mike Couturier called the crime scene "catastrophic."

Police said Thursday that detectives have processed the crime scene, interviewed many family and friends, and collected evidence. The State Medical Examiner Office also conducted autopsies on all of the bodies.

The investigation remains open.