Second I worked in a computer store where police would come in all the time and hang out for hours. I've taken hundreds of smoke breaks with them (I don't smoke but I'd stand out there with them and talk).
Third I work at a boys home for troubled children. The cops come by about twice a week for various infractions (usually involving drugs) and since I know many from my previous job I talk to them all the time even now.
Having all that experience the one thing I know,for a fact, is that Cops are people too and they hate when other people treat them badly (which is what repeating "no comment" or asking "can I go now" is considered). If your job was to get information from someone else wouldn't you be upset if they just said "no comment" and wouldn't tell you why they were saying it or even if they had the information you were looking for? The cops feel the same way and explaining exactly why you can't talk to them and giving them your word that you don't have the info they're looking for will help your relationship with them.