You probably don't need to but you should. When in a foreign country other than the U.S.A. my passport is on my person unless I'm in my hotel room. It's come in handy for a variety of everyday events such as going to a casino, roadside checkpoints, changing money, using a credit card and was very handy to have on a couple of more exciting occasions. A folded photocopy might have worked as well but I have no intention of finding out. A photocopy is kept at the hotel in the event I need to replace my passport.