Call vital records and get the home birth packet. Requires Either a proof or pregnancy OR a prenatal record. I kept my own stats so I just filled out their form and had it notarized. I didn't even have everything they looked (for instance never heard fetal heart tones so just literally wrote in: tracked movement not tones cause of position). We needed to notarized witnesses that it was a live birth. My husband did one and my friend who wasn't there til after the birth did the other. We had no problems. There was a box to check for SSN request as well.
It was the exact same process as when we had a home birth with midwives. My husband was the "attendant" both times.
Follow these instructions (I’ve done it twice) and take it up to vital records office, if you wait longer than 6 months you must go to court to obtain.