The short answer: Yes, it is legal to operate your radio in the car.
Long answer: Governor Jerry Brown recently signed into law AB-1222, which clarifies that operating mobile is still legal. Hams in California had been concerned about a law passed last year that seemed to ban operating amateur radios in cars. The well-intentioned law, AB-1785, was meant to cut down on accidents and deaths from distracted driving, a growing problem. The target of the law was, obviously, driving while using mobile phones. But the language in AB-1785 was broad and could have been interpreted to ban ham radio use as well.
AB-1222, signed on September 26, removed the terms “specialized mobile radio device” and “two way messaging device” as prohibited devices.
Here is a quote from the Assembly Transportation Committee bill analysis:
“The author believes AB 1785 inadvertently included devices that were not intended to be included in the wider cellphone ban. Devices such as two-way radios functioning on business band or civilian band (CB) radios which have a more limited scope of functions, and thus, a more limited potential for distracting a driver. … According to guidance issued by the California Highway Patrol, a radio installed and mounted in a vehicle with a wired hand microphone, for example, business band or CB radio, is not considered to be wireless communication device, nor is it considered a specialized mobile radio device, and therefore not subject to enforcement under AB 1785.”
Many thanks to the local ARRL chapters who reached out to their state representatives and made sure this important clarification was passed. The quote above was taken from a useful post about AB-1222 by Andrew Silvester KC6O of the Sacramento Valley chapter. (They also have a post about how pot grow lights interfere with ham radio because, you know, Northern California.)