CATCH-22

So I really love the book so far, but I have a question: Is the "dead man" in Yossarian's tent real? It seems to me that Yossarian is crazy so you have to watch how much you believe of his stories and tellings of things. He tries to make his stories as crazy as possible so that the reader believes that everyone but him is crazy. That being the case, it's hard to tell what really happened at what didn't. So I'm trying to figure out if the dead man in his tent is real or not. If it isn't, McWatt wouldn't be able to use the dead man's gun to shoot mice at night. But then again, maybe that's really McWatt's real gun and Yossarian's just trying to come up with another crazy story by saying McWatt stole the gun from a dead man...