What should you do? You should get an attorney. You should talk to a bondsman and be ready to post a substantial bond to remain out of jail. I am slightly hopeful that nothing will come of this if you have not already been arrested and put in jail. But it could all come crashing down tomorrow. Be prepared.
Such cases are always very difficult. Yes, they often boil down to "he said, she said." So, if the case goes to trial, it's a matter of who the jury finds more credible. If the prosecutor cannot prove the case to each and every juror beyond a reasonable doubt, you will be acquitted. If the jury believes her, you will be found guilty. Rape is, of course, a very serious offense. However, where the accusation is utterly false, there may be no reasonable alternative to going to trial, with all the attendant risks. Each person makes their own evaluation of that situation.
It was a mistake on your part to talk to the police without an attorney. Now they have at least a partial "confession" and that may help make the case against you. Stop talking to police and stop talking on public bulletin boards. Don't discuss with your friends or family. The only person you should be discussing your case with is your attorney. Never again talk to the police without your attorney present and listen to your attorney when he tells you not to say anything. If you do not have an attorney yet, get one. You want an experienced local attorney, one who is not afraid of a trial and has substantial trial experience, preferably in sex offense cases.
Note that a polygraph is not admissible in court in any state I know. These tests are not reliable enough for evidence. If you passed, it might help your attorney in negotiations with the prosecutor. If you failed, at least it can't be used in the prosecutor's case.
DISCLAIMER: I do not practice in WA. This answer to a short question is provided solely for general informational purposes and based on general legal principles and court practice. This answer does NOT constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.
Agree with previous poster. You need to lawyer up right now. If you cannot afford private counsel, you should talk to Department of Assigned Counsel. The attorney I know with the best track record for acquittals on rape/abuse charges is Jennifer Apitz. Her number is 206 321 7072. She's familiar with most courts in Western Washington.
Hope this helps. Elizabeth Powell
The previous answers are absolutely correct: you need to get a lawyer and stop talking to anyone other than that lawyer about what did or did not happen.
A lawyer experienced with trying sex offenses also can conduct investigation to discover evidence that may help prove the accuser is lying. That investigation should occur as soon as possible while people's memories are fresh. Sometimes tangential witnesses, like a cab driver, a store clerk, or someone else who saw her shortly after the encounter, can provide invaluable testimony. Sometimes the lawyer can get that evidence to the detective, or to the prosecutor before a final filing decision is made.
Understand that rape is a very serious charge, carrying a significant prison sentence and registration as a sex offender potentially for life. You must treat this accusation very seriously.