California does not record the serial numbers of guns only the sale. Technically there is no law that firearms owned before the Department of Justice’s Automated Firearms System was created. However there are penalties for not registering previously owned firearms with the Department of Justice’s Automated Firearms System.
Most states do not require owners to register their firearms with the police. A few states only require that certain types of firearms maybe registered, such as assault weapons. Registering your firearm involves fingerprinting, recording the gun's serial number, your name, and address.