The main meaning of "czy" is to point out that we have a Yes/No question. In most questions it can be omitted, but I guess it's better for learners to use it, also it's better to use it in some more formal conversations.
However, I think it wouldn't be a good idea to omit it here, after all the question is already a bit unconventional and it could change the meaning a bit. "Czy ty nie jesteś kobietą?" seems like "you are a woman, right? I was almost sure, now I have some doubts, but you are one, right?" while "Ty nie jesteś kobietą?" would sound more like "I was sure that you are a woman and now I'm shocked that you are not". At least to my ear :)
You can also find "czy" as "or" in questions. "Wolisz zupę czy pizzę?" = "Do you prefer soup or pizza?"