Copy of original birth certificate

Does anyone know how I can get a copy of my original birth certificate? I was born in Vallejo, CA in 1964. I've looked on line but can't find anything. From what I can see I can't get anything but a copy of what it is now. The reason I'm asking is that when I was a child I remember seeing (snooping) through some of my parents paperwork. There was something that said 'adoption' and had my name on it. I didn't think much about it because I knew I was born before my parents were married. Maybe it was. I guess I'm at a point of wanting to know if I do have a different biological father than the one that raised me.My parents won't admit to anything. My mom lied to me about how long they were married until I was an adult and only admitted it because someone else had told me.