TULSA, Oklahoma - Police are looking for a man they say shot and killed his girlfriend early Thursday outside their home.  

Detectives identify the suspect as Jose Gomezbaca, 25. Family members tell News On 6 the victim was 26-year-old Elizabeth Rodriguez. Police say she was sitting in the back seat of a car in the 8000 block of East 2nd Street near Memorial Drive when she was shot.

Police say the couple's two young children were asleep in the home. Family members say they are trying to find a way to tell the children their mother is dead.

Officers got the call at about 1:20 a.m. but by the time they arrived, the victim was already dead and Gomezbaca was gone.

Rodriguez's brother said he and their mother were also sitting in the car when Gomezbaca opened fire. 

Sgt. Dave Walker says officers encountered the couple Wednesday evening and were able to resolve some issues, but he says it appears Gomezbaca surprised his wife when she returned to a home the couple had shared early Thursday.

"Evidently, there's an ongoing domestic dispute where she's leaving him or he's leaving her," said Police Sgt. Dave Walker.

This is Tulsa's 42nd homicide of 2017.

Sergeant Walker says Gomezbaca is armed with a pistol and a shotgun and was last seen driving a 2004 gray Dodge Ram pickup with Oklahoma license plate 146QAO.

If you see him, police say call 911 or Tulsa Police Crime Stoppers at 918-596-COPS.

Family members say Gomezbaca may be headed to New Mexico.