Of course they can hurt you, just like a cat can scratch you or a person can slap you. If you are thinking of germs then, yes they can, but it is unlikely to happen and pet mice don't have them at all if cared for properly. Actually, they usually get their germs from people. Oooops!
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Only if they were traumatized when they were babies or put under unduly amounts of stress. I had one and it bit me-- only because we got it when it was old and stuck in its ways. Normally, however, mice will never bite you if you are devoted to keeping them happy.
i would say yes and no because when a mouse bite a fruit sometimes it does not necessarily infect the fruit