You do not need to have any DMV paperwork with you to get a smog check. The smog technician can simply enter the required information, your vehicle's vehicle identification number (VIN) and license plate number, into the smog machine.
Having the DMV renewal notice simplifies the process for the smog technician as he or she would be able to scan the bar code on the DMV document which would automatically enter the required information into the smog machine. Note: Some stations may charge an additional fee for the time required to manually enter your vehicle's information.
