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.