From Stephen Wilder, New York: 
" Your reference to the Roma reminded me of the derogatory word gyp, to cheat. I had always assumed that this was a racial epithet from gypsy and was a reference to their supposed means of supporting themselves through petty theft and deceit. However, someone recently informed me that there is in fact no connection at all and that the term has a separate origin (which he did not recall). Where lies the truth ? "

The confusion you mention may lie with another sense of the noun, for a college servant at the University of Cambridge (the English one). Though gyp in this sense is also sometimes said to come from gypsy, it may equally well come from the obsolete gippo, a menial kitchen servant; this once meant a man's short tunic, from the obsolete French jupeau. ( gyppo, as a modern derogatory term, does seem to come from gypsy, or at least, from the same source as to gyp.) 

Even if the verb does come from gypsy , most people who use it probably don't link the two ideas. It's a connection that has become stronger as we have become more sensitive to possible racial slurs, as a result of which the possibility of offence is treated more seriously than evidence of actual offence warrants. ( Much the same process has happened with "squaw" ). 

Incidentally, the word gypsy or gipsy itself was given to itinerants in Britain when they arrived from continental Europe in the sixteenth century; the word is a contracted form of Egyptian by a process called aphesis. It was thought that the people came from Egypt but they really have their origin in north-western India. Their language can be traced back to Hindi, Punjabi and Sanskrit roots, though with a lot of input from other languages that shows they spent extended periods in Persia and Armenia, among other places. They probably entered Europe via Constantinople in the fifteenth century.