It depends. Are you looking to collect child support? If you are, then he will have to prove paternity (via a blood test... If it is proven he is the father, he has to pay for the test, if not, then the state keeps looking for the father until they find him- im sure you know he is the father, just letting you know the procedure)... That usually onsets the visitation procedures...
If you are willing to dismiss child support and you dont put his name on the birth certificate, he will have to take you to court for rights, meaning he would have to go thru the paternity test procedure there too...
Most men dont bother to fight for rights... But if he wants rights, he has to go to court to get them. You can usually get free legal counsel to represent your child in the event that he does do this...
Until he takes you to court, proves paternity, and the courts have it in writing... He doesnt have rights...