Y'all are really not getting what I'm saying here. And yes, as a matter of fact, Illinois is one of the states pg1067 mentioned, (I did look it up). But the question the OP asked at least implies a belief that a cop is somehow not allowed to have relationships.

OF COURSE there's a problem if he's using the power of his position to obtain sexual favors, or whatever. That's so obvious I didn't think it needed to be said, and it's a sad thing that the world is such that anyone else did. But there is not a legal problem SIMPLY BECAUSE HE IS A COP AND FOR NO OTHER REASON. Which is the question the OP asked. Or at least how I interpreted the question as he asked it.