"Murder, He Said!"--ID this film, singer

In Crimes and Misdemeanors, Woody Allen is watching old film reels from the golden age of Hollywood musicals. One of them, in a bit of foreshadowing, is a girl singing “Murder! He said.” (I’m totally grooving on Tori Amos’ cover of it on the Mona Lisa Smile soundtrack). Can anyone tell me who the original singer is, and in what movie she sings it? I know this must be common knowledge in some circles, but both Google and Wikipedia let me down.

It was Betty Hutton in a movie called Happy Go Lucky
Here’s the video on Youtube.

Ps. It’s “Murder, He Says,” (not “said.”)

Well, that explains it. Thanks!