If both parents share custody, does either parent pay child support?

Yes. In Michigan both parents are responsible for the support of their children. The court will usually order the higher-income parent to pay child support to the other parent.  The only time one parent would not pay child support to the other parent in joint custody cases is in the unusual circumstance where both parents have exactly the same income and share exactly the same number of overnights (i.e., 182.5) with their children.