Be it a bug or intentional easter egg, there's a very interesting part of Luigi's Mansion. During the blackout that happens after the Boss battle of Area 3 on the balcony, Luigi journeys to the Telephone room and answers two calls.
During these calls, while Luigi is holding the phone to his ear, wait until there is a lightning flash and you will find that Luigi's Shadow has been distorted in such a way that it looks like he has been hanged.
Some speculate that this shadow is evidence of a much darker game than what was released. Taking into consideration that the beta footage showed a lot of spooky elements that were removed in the final release, it's entirely possible that this was one of those things that was left in from the beta version. Since the Luigi's Mansion footage was used to initially show what the GameCube was capable of, it's possible it wasn't originally supposed to be a full game on it's own.
Others take a more philosophical approach to the shadow and say that Luigi was really dead all along and the shadow shows how it happened.
Another theory suggests a lighting glitch. Because of the dynamic shadows used in the game, the shadow appears this way because of the camera angle. When Luigi answers the phone, the camera is angled up slightly and zoomed in. Assuming that the lightning strikes in-game are originated from the camera position, Luigi's shadow is lifted off of the ground, and angled to seem as though he was hanged. Nintendo's official statement cites this as the correct explanation.