Naked Murderer
This is morbid but… guy kills girlfriend after a fight at her house. Because he is smart, he then takes off all his clothes, leaves them on the bed next to her body, and sets it all on fire to destroy any incriminating evidence.
Because he is really dumb, he does not realise until after running naked to his car that he left his keys in his pocket. Because he is REALLY REALLY dumb he runs back inside and tries to somehow retrieve his keys from his burning clothes.
Becomes overcome by smoke and jumps out the window. Police find him lying outside with burns. He claims he was coming to visit his girlfriend, saw the house was on fire and ran in to try and save her. Is asked “So….why are you naked?” Cannot answer.