Officials say the gunman appeared to select his targets randomly, with the shooting breaking out at a home in the rural community of Rancho Tehama.
The incident is said to have happened in the early hours of Tuesday morning.
Officials believe the shootings started as a "domestic violence" incident and later moved to the exterior Rancho Tehama Elementary school.
A student at the school was shot and another child was hit in a truck along a road.
A woman driving the truck was also struck and all three were being treated for injuries, along with about seven others.
No children were among the fatalities.
Police said a semi-automatic rifle and two handguns were recovered from one of the crime scenes.
The shooter, who was shot dead by police, has not been identified and his motive is not yet known.
A resident only identified the gunman as Kevin, adding that his roommate was among the victims and that the shooter stole his truck.
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"Unfortunately, he's not good. He's dead, he didn't make it.and for his family, and everything like that, you know, I feel bad. We'll be there for them. UmI don't knowI just like maybe there should've been more effort put into potentially stopping things like this."
California Governor Jerry Brown issued a statement saying he and his wife were "saddened" to hear about the violence.
Ro Aram, Arirang News.