From the University of Kentucky:
Technically, you aren't required to show ID [to the police] unless you're being arrested, ticketed, or you're driving.
http://www.uky.edu/SGA/pdf/police_at_your_door.pdf
There was a recent Supreme Court case (Hibel v. Sixth Jud. Dist. Ct. of Nev.) upholding the right of law enforcement officers to ask someone to identify themselves, but from a brief skim of the decision, it doesn't seem to address the issue of any sort of an ID document.