- This mystery is considered solved.
In Luigi's Mansion, Luigi's shadow is displaced above the ground in certain situations, which can cause it to appear suspended from the ceiling.
The most widely known instance of this occurs if lightning flashes while Luigi is answering a call in the Telephone Room. It can be reproduced in some other situations where the camera is zoomed in on Luigi, such as when he is talking to certain Toads or to E. Gadd over the Game Boy Horror.
This was changed in the Nintendo 3DS remake of Luigi's Mansion.
This seems to be a lighting engine glitch. The position of the light source depends on the camera, which is normally at a fixed angle throughout the game, but is unusually low in the circumstances required to reproduce the glitch. If the camera and light source are tilted slightly upwards, it follows that Luigi's shadow would displace to an angle above the horizontal.
The glitch is most likely absent from the Nintendo 3DS remake due to the lighting system being rebuilt.
Many players interpreted the displaced shadow as Luigi's body hanging from a noose. This led to theories that Luigi is dead and the events of Luigi's Mansion are related to his afterlife.