4 weeks after on campus interview - ask about update
It's possible that they simply haven't yet finalized their ranking, gotten approval,  and made the first offer.  It seems more likely or that they have done so and you weren't their first choice.  You can certainly ask what the status of the search is, and they'll probably tell you whether or not an offer has been made, but don't expect to be told who has been made an offer or whether you're still in consideration.  

If you are still under consideration and everyone ahead of you on the list turns down their offers, then you might get an offer later.