Does Church-State Separation Preclude Police Force at Religious Universities?

In a story I'm still trying to wrap my head around, Davidson has become the 3rd religiously affiliated University in North Carolina to have its campus police force stripped of law enforcement powers after a state appeals court ruled the arrangement is an unconstitutional entanglement of church and state. A 4-3 decision by North Carolina's Supreme Court in 1994 established the precedent that ensured the outcome in this case, much to the chagrin, it sounds like, of the Court of Appeals.

The author of Tuesday's ruling in the Davidson case, Court of Appeals Judge Jim Wynn, said his panel had to follow the earlier precedents despite evidence that Davidson "is primarily an educational institution with well-established principles of academic freedom and religious tolerance."

He also urged the Supreme Court to hear any appeal.
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It hasn't revisited the issue since deciding the Campbell case on a 4-3 vote. In 2003, it refused the attorney general's request that it hear an appeal of the Pfeiffer case.