Randolf has a mustache and appears to be wearing a jacket, scarf and a hat.
Events of Criminal Case
Randolf's brother, Theodore, had been murdered prior to the events of the game. According to Catastrophe Joan, Rose—who was a bounty hunter at the time and was investigating the murder—had relentlessly beaten Randolf, whom she believed to be the criminal, until he was forced to admit that he had murdered Theodore with a pickaxe in the gold mine, getting him jailed as a result.
With Joan accusing Rose of beating a confession out of Randolf, Isaac and the player went to investigate the gold mine, and unearthed a human skull. Per Dick, the skull belonged to Theodore and its wound was consistent with a pickaxe, thus proving Rose's hunch to be true. With Theodore's murder solved, the team denied Joan's version of the story and saved Rose's reputation, although her methods were questioned.