There is obviously more to this story, and either you are leaving it out to keep from looking bad, or else you don't know.
However,
I would theorize that the girl had developed an obsessive relationship with you, and when you did not appear to reciprocate those feelings she had for you, and further when you spurned her feelings by bringing other girls over and having them spend the night, you have created a monster. With the unstable condition that you describe this girl as being in, I think it is fairly easy to spot two likely conclusions here:
Either...
1. The girl lost it after you told her to F off, and immediately called her mother and told her something along the lines of "he got really mad at me and hit me" or "he got really drunk and forced himself on me." You returned the next day and apologized, and she accepted your apology, but not before it was too late.
Or...
2. You really did either hit her or engage in some type of sexual activity with her. If the latter is correct, she may have wanted it at the time, but became so distraught after your fight that she took some of the truth and twisted it into something like rape.
The only two things I can think of that could possibly illicit this type of response from her parents would be physical or sexual abuse, either imagined or real.
Not saying you really did it, rather that I think you've been accused of something serious and are oblivious to it.