Why would you think the police would care about this sort of agreement?
You cited a law that makes it legal (assuming the sort of order mentioned in the law exists), so I'm not sure I really understand what you're asking.
If DCS is involved it means either that the mother obtained a child support order or that she received public aid for the child and DCS obtained the order in order to recoup the cost of the public aid. Either way, your "agreement for zero child support" is legally meaningless.

