I read a good fan conspiracy theory, that it was a two man job they planned together, and they kind of looked alike- one dude did the deed, the other sloppily went on the run while the first one escaped. Luigi was the fall guy, but is actually innocent, and he can prove it in court, while the actual killer is chilling on a beach somewhere. And that would, allegedly, be why Luigi seems so relaxed about the whole thing. Because he knows he's gonna walk. Kind of like an inverse "The Life of David Gale" maneuver.

I don't know if I believe it, but it's surely a possibility, and it's an interesting take. :)