Hey mama, and welcome to MCD!

I have never "met" another AL UC'er before!
Alabama actually makes it very, very easy to get the birth certificate. They have a "homebirth packet" that you can request from the state department of records in Montgomery. I have all of the specifics saved somewhere, I will dig around tomorrow and try and find a phone number for you.
All you have to do is fill out the packet information before your child's first birthday and mail it in. You never have to do a face to face with anyone.
They do require you to have "proof of pregnancy" and "proof of live birth".
What I did was go into a CRNP's office and take a urine pregnancy test around 8.5 months pregnant. I told her what it was for, and she agreed to write up a statement saying that yes, I was pregnant, and she estimated my child to be born at such and such time.
I took my son back to see her when he was about a month old, and she looked at him - didn't weigh him, poke him, prod him, nothing - and wrote up another statement saying that yes, she believed him to be my baby and he was in good health.
I sent those two statements back to Montgomery along with the homebirth packet, and I got his birth certificate a few weeks later in the mail. I took that down to the social security office and got his number within minutes, his card in the mail a few weeks later.
Even though homebirth midwives are not allowed to practice legally in our state (there is actually a bill before the house right now trying to change that) Alabama really doesn't make it that difficult to get things done, in my experience. I didn't have anyone (official) bat an eye at my method of birthing.
I am pretty sure I have the homebirth packet saved on my computer in PDF form - let me look and if I do I will e-mail it to you.
Feel free to pm me if you have any more questions or if you need any referrals to doctors and such. We don't do docs or peditricians in any form, ever, but there are a lot of women in Alabama that have homebirths with midwives, and I have never heard any horror stories of docs/pedis not seeing them because of it.
Good luck, and again - welcome!
