The name of this crewman, who falls off of Circe's roof while he is drunk, is Elpenor. This happens in Book X of "The Odyssey."
The crew of the ship (other than those who were killed by Polyphemus the cyclops) have been on Circe's island for about a year. At first she turned them into pigs, but then Odysseus forced her to change them back and she was a good hostess the rest of the time.
Odysseus finally decides it's time to go and tells the men. But Elpenor is drunk (and is not very smart to start with). When he hears the men bustling around, he jumps up and "forgot all about coming down by the main staircase, so he tumbled right off the roof and broke his neck, and his soul went down to the house of Hades." They will see him there in the next book.