The Hat (1962)

Snuffy, Barney and Louise are stranded in the big city with no money for a mule and a wagon until a pair of gangsters offer to buy them one if they will just deliver a note and a satchel to the nearby bank. Desperately in need of funds to return to Hootin' Holler, Snuffy gets a job helping out the men by standing guard outside of a building... not realizing that he's becoming an unwitting pawn to a pair of bank robbers. The chase is on. The only clue to the robbery is a photograph of Snuffy's hat