What you are really asking here is what is the jurisdiction of the campus police.  In other words, how far reaching are their powers in the fulfillment of their duties.  Campus Police officers have the authority to enforce state laws.  In trying to ascertain the applicability here I came across a whole set of laws that deal with the different universities and colleges in Illinois - for private colleges, for state universities, or Northwestern specifically.  I am leery just like you.  So if they are demanding entrance - for activities that would either need your permissin or a search warrant - then politely decline.  If there is an issue later on consult with a campus legal office.  Good luck.