Child support if living with the father?...

Hello everyone! So I live in Michigan, and I know I need to seek legal advice on some of these things but I am curious if anyone in here has some experience first. So, long story short I am 8 months pregnant and I am living with the father, even though we broke up and no longer together. It’s very awkward. Well, I do not plan on him signing the birth certificate, and baby will get my last name. He is demanding a paternity test so I’m sure he will be doing that after she’s born. So, with him taking a paternity test, does that give him rights? Also, since we aren’t married and not even together, will they still make him pay child support even if we are living together? Thank you all!