Fairfield police say the woman was in a car when she tried to get the attention of an officer, saying she was being assaulted and kidnapped.
The car drove off, with the officer in pursuit. The driver crashed into several other cars a few blocks away.
Officers then discovered the woman had shot the driver during the incident. He later died of his wounds.
A 10-month-old child was also in the car, but was not hurt.
She was taken to the hospital with minor injuries.
The crash happened at the intersection of Travis Boulevard near Dover Avenue.