San Diego police are asking for help locating the suspect in Tuesday night's fatal shooting in the Midway District.
Police said Joe Bennette Conway, 41, shot a woman around 11:45 p.m. Tuesday in the parking lot of the Barons Market on the 4000 block of West Point Loma Boulevard.
Conway then fled in a red Chevrolet Cavalier sedan, possibly with Arizona license plates, San Diego police Lt. Anthony Dupree said.
When police arrived they found a woman with a gunshot wound in the upper body. She was transported to the hospital where she later died.
The woman has been tentatively identified but police won't release the info until her family has been notified, Dupree said.
An employee at the nearby Domino's Pizza said the woman and Conway came into the pizzeria as a couple where the woman asked to use the bathroom. When she came out, the two went outside to talk.
The conversation turned into an argument and minutes later, a single gunshot was heard, the employee told NBC 7.
The victim was still alive when the employee ran out to help but she was unable to speak.
She died at UC San Diego Medical Center around 2:45 a.m. Wednesday.
Conway is 5-foot-7 and weighing 150 pounds, police said. He was wearing a dark blue, button-down shirt, black pants and sandals at the time of the shooting.
Anyone with information on the whereabouts of Conway was urged to call the SDPD Homicide Unit at (619) 531-2293 or Crime Stoppers at (888) 580-8477.