Collect and keep safe evidence proving your position. Were you injured in a car accident?You should call your own insurance company first to let them know what happened. Make this call on the day of your accident if possible. California law requires you to have bodily injury liability insurance in case you injure someone in a car accident. It pays for the other party's damages. In the state of California, the statute of limitations to sue for car accident injuries is two years. California is an at-fault state for car accident claims. Therefore, state law requires drivers to maintain a minimum amount of liability insurance coverage. California sets the statute of limitations on injury claims at two years.