"Jim Crow" was the character created by a white minstrel show performer named "Daddy" Rice. He was reputedly popular on the stage. His song was something like "Turn around, turn around, jump real slow, every time I turn around I jump Jim Crow" or something to that effect. The tune is sort of doggerel I think but apparently the act caught on hence the name.

There is an early jazz tune called the "Jimtown Blues" which probably is a derogation for the black section of town.

Frank