I am a Maryland practitioner but will try to handle this one. Medical bills generally ARE dischargeable in a Chapter 7. Now where this is tricky is that it is for the birth of YOUR child. If this can be seen as any kind of child support, then no.
However, let a court tell you that you are wrong. I suggest you put the bills on the bankruptcy, following the rule that generally medical bills are dischargeable. Unless there's some Local Rule in Michigan I am not aware of, I think this is a good strategy.
Have you retained an attorney for your Chapter 7 bankruptcy? If so, consult your attorney.
The debt is likely dischargeable, however. Administrative and other governmental fees that do not fall into the specific categories of debt, such as recent tax debt or unpaid child support, etc., that the Bankruptcy Code explicitly excludes from dischargeability are just as dischargeable as any common credit card debt.
If you've already filed and haven't scheduled this debt, you'll need to amend your schedules to list it and properly notice the creditor (State of MI).
Medical bills are generally dischargeable in Bankruptcy. I am not sure why the "charge was ordered by a judge". Did the judge issue a judgment for the creditor? In any event, it is your duty to add the creditor on your schedules. Follow the local rules when amending.