Paternity and Custody Rights

I recently had a baby. The father was not present so he didn't sign the birth certificate, nor has he come to see her yet. I'm in NJ he's in MI does he have legal rights to her? I'm afraid that when I petition for custody that he will also try to do the same and it will go into this long drawn out process. She has his last name. But us there a chance he can take her from me??

Please advise if possible

He has no rights until he is determined to be the father, whether by court action or affidavit. He will be able to seek visitation, and could conceivably petition for custody, once determined to be the father. He would also be obligated to pay support. In most cases, fears of a custody challenge are overblown, particularly where the father hasn't been even trying to see the child.