Is it possible to get a free paternity test?

Q: I have a friend who has a girlfriend who is pregnant. He doesn’t want to be with her anymore, because she has knowingly cheated, but he doesn’t want to jeopardize being part of the child’s life. He wants a paternity test but can’t afford it. Would she have to pay for the doctor bill and the paternity test if he asks for her to get one?
He wants to gain custody of the child, but doesn’t think he should pay to find out if it’s even his and to be honest, I agree with him. He lives in Michigan. Any information would be great. Thanks!

Additional Details
She’s underage and dropped out of school with no job. She refuses to see an OB/GYN and doesn’t take her prenatals. Her mother is addicted to drugs and the girl isn’t in a good environment at all, and the baby will have it worse off. Which is why my friend wants to gain custody.

A: Seeing how she is underage and knowing she is pregnant and where she is staying is not good, he could call CPS. Explain to them his position that he believes he may be the father and he wants responsibility. He can try contacting the health and human services department, or even the police station just to get a start. But i think CPS is the way to maybe go. He if goes through the courts no matter what there are gonna be fees, for the court, and the dna test but they could possibly work out a payment plan. Seeing how at least he is making an effort to do the right thing if that’s his child.