This is a cool idea for a mystery novella or short story, but I suspect this would be very hard to pull off well as a Play by Post roleplay.  My experience is that PbP Roleplayers are prone to metagaming, so unless the writer of the culprit could manage to write their character without cluing in the other players that their character is the murderer, then somebody would likely come to the conclusion that that character is the murderer even if their character wouldn't have sufficient evidence to come to that conclusion.