Investigators are searching for a woman who may hold clues to the background and history of the man who shot and killed two Santa Cruz police officers on Tuesday before being gunned down in a shootout with police.

Terisa Johnson, aka Terisa Lamb, 28, was not involved in any way with the murders of Detective Sgt. Loran "Butch" Baker and Detective Elizabeth Butler, Santa Cruz County sheriff's officials said Thursday.

However, Johnson is thought to have been acquainted with or in the company of the suspect Jeremy Goulet earlier this year and investigators hope she can provide information on his background and social history, officials said.

Johnson's current whereabouts are unknown. She was last known to be homeless and living in a camp in the city of Santa Cruz, and is known to frequent the Santa Cruz, Live Oak and Soquel areas.

Anyone with information on her whereabouts is asked to call the Santa Cruz County Sheriff's Office at (831) 471-1121 or ask her to call that number.

Goulet, 35, allegedly shot Baker, 51, and Butler, 38, around 3:30 p.m. while they were attempting to interview him as a suspect in a misdemeanor sexual assault case.

The two veteran officers were standing at the front door of Goulet's apartment at 822 N. Branciforte Ave. speaking with him through a closed door for less than 10 minutes when he "disappeared" from behind the door, Sheriff Phil Wowak said.

Goulet then allegedly shot the two officers with his .45 caliber handgun, picked up their handguns, went to Baker's car and put on the officer's body armor, Wowak said.

He drove a short distance to Doyle Street, but it was blocked at the time by a Santa Cruz Fire Department truck, so he attempted to flee on foot.

Officers responded to the scene and moments later, Goulet started firing two handguns at six officers, four of whom returned fire and killed him, Wowak said.

Upon reaching Goulet's body, police found he had three handguns -- the officers' guns and his own -- his passport and a ticket for a flight to New Mexico leaving later this week, Wowak said.

A public memorial for the officers is planned for next Thursday at 11 a.m. at the Kaiser Permanente Arena, with the Santa Cruz Civic Auditorium holding any overflow crowds from the event.

There will be a motorcade procession from the county fairgrounds at 2691 E. Lake Ave. in Watsonville to the arena prior to the memorial.

Santa Cruz police took two days off from patrol duties after the shooting but returned to duty today. Patrol shifts were covered by sheriff's deputies and the California Highway Patrol.