The North Carolina Court of Appeals addressed a very interesting question in a case involving Davidson College (NC v. Yencer):
Whether it violated the First Amendment to delegate state police power
to a religious institution, and in particular to its campus police
force. 

The NC Court of Appeals held that it was unconstitutional.

If not for past NC Supreme Court precedent, the Court likely would have come up with a different conclusion.

I wrote more about this important case here.