An Amtrak passenger train crashed into a four-door sedan at a crossing without a train signal or guardrails in a rural area of the East Bay in Northern California on Sunday, killing three people and critically injuring two others including a child, a spokesman for the local fire department and emergency services said.

The victims were pronounced dead at the scene, Steve Aubert, a fire marshal with the East Contra Costa Fire Protection District, said in a phone interview.

The injured child was taken to a hospital in an ambulance, but the injured adult was transported for treatment by helicopter, signaling that the injuries might have been life-threatening, Mr. Aubert added. He called both injuries “major.”

A spokeswoman for BNSF Railway said that the crash occurred at about 1:15 p.m. and that “approximately” five people were injured in total. Mr. Aubert said that he was aware of only two injuries and that nobody on the train had been injured.

The five-car train was carrying nearly 90 people, a spokeswoman for Amtrak said in an email.

“Amtrak is working with local law enforcement and BNSF, the track owner, to investigate the incident,” she added.

Such accidents, she added, “serve as critical reminders about the importance of obeying the law and of exercising extreme caution around railroad tracks and crossings.”

Two employees of John Muir Health, the hospital where the injured people were taken, declined to comment on their status.

The people in the sedan were traveling from an event in the area that about 150 people attended, Mr. Aubert said.

He described the crossing point, on a dirt road in a largely agricultural area in Brentwood, about 60 miles east of San Francisco, as “highly potentially dangerous,” saying that emergency services responded to accidents involving trains and smaller vehicles at least once or twice a year.

In recent years, the area has regularly been the site of Amtrak collisions that led to serious injuries, close calls and demolished trucks.

Even though there are no guardrails or signals at the crossing, trains are allowed to go 80 miles an hour, Mr. Aubert said.

“If you’re not careful and if you’re coming down the track,” he added, your car and a train “can come together quite rapidly.”

April Rubin contributed reporting.