Does the county your baby is born in automatically send you their birth certificate?

Social security cards are automatically sent out within the first month or two after you have your baby but birth certificars they do not send it to you... I live in California and I had to go for my sons birth certificate at the courthouse where the recorder room is and that is where you get birth/death certificates and it was $18 for my sons. You also have to go to the courthouse in the county that your daughter was born in so if you've moved out of the county then you have to go back there to get one, or also check to see if they have an on-line website for that county and try to purchase it on there. Hope this helps! =]