James Jones killed Jacob Williams.
When she was shown the scene of the crime, Detective Carr realized something was missing. Jacob Williams was preparing to go to a formal dinner, but nowhere in the room were the white dress shirt, bow tie, or studs he would need for his tuxedo.
Then she remembered the smear on Williams' hand. Nothing in the room was found that indicated where he had wiped the hand. She realized that after he was shot, Williams must have clutched at his wound, getting his hand bloody. Then he wiped the hand on the closest thing he could - his killer's clothing.
The killer certainly couldn't leave Williams' room with bloody clothes, so he removed them, burned them in the fireplace, and put on Williams' shirt, tie, and studs.
The only person in the group in a tux was James Jones, so Carr deduced he was the killer.