According to AOPA, California requires liability insurance, but does that apply to experimental aircraft? When I called EAA, they thought only Minnesota required insurance.
The short answer is no, the State of California does not require insurance. But there is a catch. If you base your airplane at most public airports the municipality may require coverage. My hangar lease requires $1 million liability coverage and if you want the ability to drive your car on the ramp you need the same amount on your auto policy.