The shooting happened at or near an elementary school in Rancho Tehama around 8:00 am. local time. The building was evacuated and students moved to a safe location, police said.
An employee with the Corning Unified School District said there were reports of an active shooter at the school, and there were confirmed injuries.
The suspected gunman was shot dead by police and at least two victims are believed to have been killed.
A 6-year-old and another child are among the injured.
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Tiffany's husband, Brian Rodgers, said another witness reported seeing a white pickup drive through the school gate and start shooting.
A six-year-old child with two gunshot wounds was reportedly taken by helicopter to a hospital.
According to KRCR TV, a witness identified only as Tiffany, who operates the nearby Coffee Addiction Coffee Shop, said she heard about 90-100 shots fired.