A very brief read of the MI Statutes would indicate that you are not responsible for your child's medical costs under the Doctrine of Necessaries as ruled upon by the MI Supreme Court in
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However, you write that per your divorce decree you are responsible for 50% of the medical costs for your child.
You need to determine what the actual remaining charge after insurance has paid. Then you are responsible for the remaining balance at 50%.
Your possible Affirmative Defenses are, wrong party, wrong amount, never received a billing statement therefore no account stated.
I don't really like your answers.
Possible solution; pay it. It's your child that needed medical care irrespective of your feelings for your ex-wife. By paying it you avoid a judgment against you. Even though you may be able to have the judgment set aside, it's simply not worth the hassle.
You can then go back after your wife for the difference. Or in the alternative, depending on the terms of your divorce decree, if you pay alimony to your ex-wife, reduce the next payment or several payments by the amount you pay her. If that remedy is not practical, the difference that is owed to you, book it as additional alimony and take the tax deduction.