That's BS. There is no law in the US anywhere that would force you to sleep with someone. Period.
Keep everything in writing. When you write out your written notice to have her vacate the apartment or house, include a paragraph that gives her a time limit for moving her stuff out of your bedroom (I'd say not more than 24 hours). Offer to help if you want to be nice.
Be sure your letter to her has your name, address, date, and signature. Make a photocopy. If you can, get her to sign your copy as "received" with her signature and date. (She may refuse).
If she refuses to sign for the letter, write out a separate dated, signed memo stating the circumstances and keep that for your records.
Paperwork is very important - you need a paper trail if this goes to court.
Some courts sell packets for evictions for a small sum. If your local court does, you may want to buy one of these and use the forms provided.
If your "roommate" will not move out of your room, or threatens you in any way, shape, or form, I suggest that you attempt to obtain a domestic violence restraining order. (This should also help you get her out of the apartment altogether). You may want to print this out (it opens somewhat slowly): http://www.state.wv.us/wvsca/familyct/DomViolence.pdf
Please let me know if I can be of further help to you.
My very best,