C.O.
If you had her at Antelope Valley Hospital, you will be able to call them and ask them.
I don't know what changes have occurred in the California state laws regarding birth certificates...
Are you changing her name or just declaring who her father is? If you are changing her name - in MY OPINION - you will have to go through the whole 9 yards....birth certificate name change, social security name change, passport name change...and anything else that you have her on - insurance, etc.
Good luck!!