Cortona is a very safe town to visit, but as is the case with most places that get a lot of tourists, you should always keep your eyes open for pickpockets. It is always when you least expect it that something happens. You should never just leave your wallet, or mobile phone out on a table, and be particularly cautious if approached by beggars or children with a piece of paper or cardboard in their hand - this is what they use to hide their thieving hands. Americans - never stick your wallet in your back pants pocket - that is inviting trouble. You have to remember that if you are pale skinned, wearing shorts and a t-shirt, or just walking around aimlessly, people will start to notice. Not everyone is out to get you, but there are some people who may try to rob you.  If you do get in any trouble, you should go to the Carabinieri office in Via Dardano, off Piazza Signorelli.  If you really need help you should go to  your Consulate or Embassy.