Can I go to the police?

Dude.....she has a crush on you if not she just likes you but is not confident and is scared to approach you. she may feel that you are not giving her much attention. So she will accuse you of things and piss you off. Your best bet is to talk to her and see why she thinks such things. If she still acts that way then she is just a woman with a 6th grade girls mind, just ignore her. Do not go to the police it will just make it worse and there isnt really anything you can do. You might be able to file a restraining order which might help but i dont think that would be a good reason dude. just ignore the brat.