Is the guy who signs the birth certificate responsible no matter what?

I live in Indiana. I have a 6 month old daughter. There is a possibility of two men being her father. One of the guys, Dustin, was there throughout the whole pregnancy and four months of her life. He signed the birth certificate, but now that he found someone new, he doesn't do anything to help out. He never tries to see her anymore, but the other guy, Alex, that wasn't there (he just saw her for the first time two days ago) wants to get a paternity test because he wants to be the father. I've heard, though, that since Dustin signed the birth certificate, he's always going to be responsible for supporting her, is that true? I'm going through the child support system now, trying to get Dustin to pay child support and they didn't even consider asking me if we needed to establish paternity because my daughter has his last name and he signed the birth certificate, but if I get a paternity test done and it turns out that Alex is the father, will they not get Dustin for it?