SANTA CRUZ, Calif. –  Two police detectives were shot and killed when they tried to question a man over a report of a sexual assault, and the man later died after a brief chase, authorities said.

Sgt. Loren Butch Baker, who was married and the father of two daughters, and Detective Elizabeth Butler, who had two sons, were shot and killed Tuesday during an altercation at the home of the man, according to police and the Santa Cruz County Sheriff's office.

They were shot while following up on allegations that 35-year-old barista Jeremy Goulet made inappropriate sexual advances on a co-worker at her home, authorities said. Goulet was arrested Friday, and The Santa Cruz Sentinel reported that he was fired the next day.

Baker, a 28-year veteran of the force, and Butler, a 10-year veteran, had gone to the house where Goulet was living to follow up on the case, authorities said. They were subsequently fired upon and called for backup, and responding officers found Goulet, who died in the gunfire that followed, the sheriff's office said.

"There aren't words to describe this horrific tragedy," said Police Chief Kevin Vogel. "This is the darkest day in the history of the Santa Cruz police department."

The shootings prompted the lockdown of two schools and an automatic police call to nearby residents, warning them to stay locked inside. The ordinarily quiet residential neighborhood echoed with a brief barrage of gunfire that killed the suspect about a half hour after the officers were shot.

A store clerk a few buildings from the shooting said the barrage of gunfire was "terrifying."

"We ducked. We have big desks so under the desks we went," said the clerk, who spoke on condition of anonymity and asked that her store not be identified because she feared for her safety.

After the shootings, police went door-to-door in the neighborhood, searching homes, garages, even closets, to determine whether there might be additional suspects. Law enforcement officers filled intersections, and helicopters and light aircraft patrolled the neighborhood about a mile from downtown Santa Cruz and the Santa Cruz Beach Boardwalk.

The city's mayor, Hilary Bryant, said in a statement that the community about 60 miles south of San Francisco was "heartbroken at the loss of two of our finest police officers who were killed in the line of duty, protecting the community we love."

"This is an exceptionally shocking and sad day for Santa Cruz and our police department," Bryant said.

Goulet, a barista at a coffee shop in the Santa Cruz harbor, was previously convicted in Portland, Ore., in May 2008 of peeping at a 22-year-old woman who was showering in her condominium and of carrying a concealed weapon, according to a Portland newspaper, The Oregonian. He was on probation but was sentenced to two years in jail after a dispute with his probation officer.

The shootings came amid a recent spike in assaults, which community leaders had planned to address in a downtown rally scheduled for Tuesday. That, along with a city council meeting, was canceled after teary-eyed city leaders learned of the deaths.

The recent violence included the killing of a 32-year-old martial arts instructor who was shot outside a popular downtown bar and restaurant; the robbery of a student at the University of California, Santa Cruz, who was shot in the head; a 21-year-old woman who was raped and beaten on the UC campus; and a couple who fought off two men during a home invasion.

The Associated Press contributed to this report