Birth certificate-kind of long, sorry!

Okay so my baby's dad isn't really in the picture, I haven't actually talked to him in a couple months mainly because when we broke up he went back to the 'hard' drugs he did before we were together. Which I obviously don't really approve of. The way we're 'communicating' at all is I'm somewhat close with his mom and she speaks to him some which is how he's getting any sonogram photos or any info as far as that. I guess what I'm getting at is if I put his name on the birth certificate but he doesn't sign it how much 'say' does he have? I feel wrong not putting his name on it which is why I'm planning to. He doesn't have a great history as far as his record goes, so I don't want him to have any custody (even though I don't think he wants any really) but I would still like him to be able to see his child.