An old movie black and white, murder/mystery. Hillbilly or backwoods girl holds clue.?

She is very naive or perhaps slow. She repeats a nonsense poem throughout the movie, but it is not until the end that the police or detectives figure out that it is a clue to who committed the crime. The poem has the same cadence as the old Lincoln, Lincoln I've been thinking...but of course with different words. First word may have been Honors or Honest.