Unlike most of the conversation trees in the game, this time, you have to say everything right to get Butler out of his office. And since you only have one coin... well, way to render the game unwinnable once again!
So let's get it right the first time. Incidentally, the voice actor for Mike decided to disguise his voice by pinching his nose. I'm dead serious.
Sheriff: Who's being robbed?
Mike: The Dairy Freeze just outside of town!
Sheriff: Thanks. I'll be there in a jiffy.
Okay, so I guess it wasn't that hard. Let's get into his office.
Don't be cracking wise, Mr. "I never heard of those riddles" Guy.
Let's look at his desk.
Nice that he kept incriminating evidence in his desk.
Okay, okay. Let's try going to Jack again.
Mike: I found a newspaper article accusing the Sheriff of graft!
Jack: Well, I'm not surprised. I never thought that fat slob was the champion of law and order he pretended to be. Unfortunately, that doesn't link him to Rita.
Mike: I also found a photo of Rita in his desk. He smashed it with his fist.
Jack: Really? I guess he still carries a torch for Rita, after all. Good job, Detective Dawson. You were right to suspect him. What else did your snooping turn up?
"But I didn't masturbate to them! Not to Rita, the pure..."
Jack: I told you he's not the grandfatherly old politican he'd like us voters to think he is. Man, I'll bet you wanted to kill the guy when you saw those photos. Find anything else?
Mike: No, Jack. That's it.
Jack: You're doing good, but you ain't finished. We gotta get stuff on all three, okay? Get back out there and keep trying. Meet me back here later. I gotta get goin'. Keep at it, Mikey.
Also interestingly, it appears returning the Light World prize to the Dark World Wheel of Fortune did this.