California law requires all registered vehicles that were issued two license plates, properly display both plates on the vehicle. Basically, all street legal cars are required to have two plates. Many times, vehicles may be purchased from dealerships that do not install a front license plate mount to the vehicle. This is not an excuse for failing to properly display and mount the license plate. A driver may be stopped and cited for not having license plates properly displayed. Some communities, like Arcadia, issue parking citations to vehicles that are parked without plates properly affixed. Simply having the plate in your car or tossing it on the dash board does not suffice.
Please install your license plates according to CVC 5200 and CVC 5201. The law was modified in 2011 to also require the plates be mounted so that the characters are upright and display from left to right. Take a look at the links provided for specific language from the California Vehicle Code.