If the father of my baby signs the birth certificate can he take the baby away since he's on the certificate?

The parents listed on the birth certificate have equal custody to the child. So no, he can't just take the baby away, that could be parental kidnapping. But you should go to court and establish paternity, custody, support and visitation.

What do you mean by take ? Go to court and file for custody and get level custody, or joint custody?

He can do that even if he does not sign the birth certificate