No, provided you are over the age of 18. California bicycle rules are explicit and require only riders and passengers on bicycles who are under the age of 18 to wear helmets. Even though the law does not require it, many bicycle operators nonetheless wear helmets for additional protection.
All bicycle riders should familiarize themselves with California bicycle safety suggestions and follow all bicycle operation laws as well. Unfortunately, no matter how careful an operator is, bicycle accidents still occur far too frequently.