Not sure if I am being beckoned as the grandson of a former Chestnut Ridge Railroad track gang foreman or a wordsmith, but in either case, I don't know the answer to the question. If I had to make an informed speculation, I would surmise that it may have had something to do with the history of segregation laws following Plessy v. Ferguson, which if I am not mistaken, were first applied to railway cars, and the slang term - derived from blackface minstrel shows, first being used by conductors and crews in and around the railway business. That seems too relevant to not have something to do with it.
EDIT: On the other hand, I have seen a number of historical references where it is hyphenated, and in lower case, like this - "jim-crow" - which diminishes the allusion to segregation, and tends to imply the "jim" part almost as a prefix for the "crow" part, which further tends to make an allusion, for me, anyway, to the long pry bar.