Comes from a derogatory minstrel routine performed in the early 1830's by a white man named Thomas Dartmouth "Daddy" Rice who performed minstrel routines in black face as the fictional Jim Crow.
A caricature of a clumsy dimwitted BLACK enslaved man was the "heart" of the routine.
There was song called "jump Jim Crow" apparently. Rice saw a black man singing that tune in Louisville, Kentucky so he used that as his device, his SCHTICK, his GIMMICK to entertain white audiences in stereotypical dialect. He was a sensation!