Drop out of PhD to do MSc So, a bit of background: I went straight from my bachelor's to a PhD with the supervisor I had for my BSc. However, I have decided I'd like to instead do an MSc at a different university. 

My question is: how do I put this in my CV. Can I put 'Research Assistant' under the Employment section? And how should I approach my supervisor in terms of asking her to be a referee?
People change programs, this happens, and your advisor may or may not be understanding and supportive depending on the circumstances of your case.

Don’t misrepresent yourself in your CV! If you were a graduate student, say that, and mention that you switched programs in your statement of purpose (saying you did so due to personal circumstances is fine). If you say you were a research assistant and mention nothing about the PhD it’ll look like you have something to hide.

Good luck!