if your neighbour is that bad, Im sure the police are well aware of her and her antics. I wouldnt worry too much, as all cases go through the cps now, who I doubt would run a case like this as it wouldnt be in the public interest. There has been no damage done, and if you were all of these things that you were accused of, the police would be aware of you too dont you think?
Anyway, if you have to speak to police about it, you could also make a statement telling the truth that nothing of the sort happened.
If there is still a problem, how about seeing a solicitor for advice about an injuction? maybe the threat of that would get your neighbour to leave you alone?