If someone is shot at closerange, doesn't it leave a burn?

I ask because I was watching a show where someone finds out their family history, the deceased in question had apparently died from a revolver gunshot wound in the back of the head somewhat behind the ear, and the result was that it was from a game of Russian roullete. However, the report of the death said there was no charring of the skin around the wound. If it had been at close range, as it would have to be to be self-inflicted, wouldn't this have caused charring? Correct me if I'm wrong, I thought that was a method often used to determine the distance a shot was fired at.