What part of Southern CA are you in? I had a UC in San Diego, which is apparently wildly different from the rest of the state as to how they treat out-of-hospital births. If you're outside of San Diego County, I'm pretty sure you just need to print the packet from the Capital's website. If you're in San Diego, and you don't have "medical evidence" of the birth, ie a midwife, doctor, or paramedics, you'll have to file a petition with the courts to establish fact of birth. Here's the link to my post detailing what I had to do to get the birth certificate.