RANCHO TEHAMA RESERVE, Calif. — A gunman driving stolen vehicles and choosing his targets at random opened fire ‘‘without provocation’’ in a tiny rural Northern California town Tuesday, killing four people and wounding at least 10 others, including a student at an elementary school, before police shot him dead, authorities said.

The gunfire began shortly before 8 a.m. in the rural community of Rancho Tehama Reserve, a homeowners association of modest houses and trailers in rolling oak woodlands dotted with grazing cattle about 130 miles north of Sacramento.

Police offered no immediate word on the assailant’s motive, but a sheriff’s official said the shooter’s neighbors had reported a domestic violence incident a day earlier.

Brian Flint told the Record Searchlight newspaper in the city of Redding that his neighbor, whom he knows only as Kevin, was the gunman and that his roommate was among the victims. He said the shooter also stole his truck.

‘‘The crazy thing is that the neighbor has been shooting a lot of bullets lately, hundreds of rounds, large magazines,’’ Flint said.

Tehama County Assistant Sheriff Phil Johnston said officials received multiple 911 calls about gunfire at an intersection of two dirt roads in the upper reaches of the sparsely populated neighborhood. Minutes later, more calls reporting shots flooded in from different locations, including a small elementary school.

‘‘It was very clear at the onset that we had an individual that was randomly picking targets,’’ Johnston said.

Witnesses reported hearing gunshots and children screaming at Rancho Tehama Elementary School, which has one class of students from kindergarten through fifth grade.

Johnston said one student was shot at the school and flown by helicopter to a hospital, and another student was wounded in a car on the way to school. He said no one was killed there.

The assistant sheriff said the school locked its doors, and students and staff ‘‘sheltered in place’’ until deputies ushered them onto a school bus and led it to safety under heavy guard.

Johnston said authorities believe they know the identity of the shooter but declined to release his name pending further investigation. He appears to have fired a semiautomatic rifle and two handguns at seven locations, authorities said.

The shooter initially stole a neighbor’s truck and then carjacked a second vehicle before two deputies exchanged gunfire with him, Johnston said. No officers were hurt.