Guessing for the OBC recording they figured most folks who were into Broadway knew where Scarsdale was but lots of 'em wouldn't know from gonif, and by the time they got to the film they figured let's assume everyone's from Salt Lake City, so yeah -- "small town."
I don't have a copy of The Complete Lyrics of Frank Loesser, but perhaps there's an interesting note about it there. (Also I'm having a thought about the alteration of theater lyrics back then for recordings, like the way they disappeared "virgin" from Carousel.)
I've managed to search-catch a tiny glimpse of the page in question, and there's the word "policeman" clear as day, but if there's a footnote on the subject it's not, alas, visible to me. (And no search I can do including Loesser, "Sue Me," gonif gets any hits at all.) (🤷🏻♂️.)