What should I do about my neighbor?

I have lived (with my wife) in our 2nd story apartment for almost 6 years. in the past couple years our property went smoke free so I decided to quit and I am still not smoking. About 2 months ago a lady rented the studio apartment below ours that the rest had been converted into the managers office. Out of no where we start getting talked to by the manager about her complaints of us smoking in our apartment. My wife smokes ONLY when out at bars and social events where others are smoking but never at our apartment. So because the property manager and assistant manager are both friends of ours, they no we are not smoking and that this lady is a little off her rocker. about a month ago we started hearing very loud bangs that sometimes shook our apartment that come from the studio below. On 6/15 there is a letter on our door typed from our neighbor telling us that our smoking in the apartment is causing her health issues and is upsetting her dogs hyperthyroid issue. I wrote her a very professional letter back stating that A. We do not smoke. B. we have 2 indoor cats that we would NEVER make them suffer from second hand smoke. C. that we both live right on a busy road and maybe she is smelling the car exhaust. and D. smoke rises. the last thing I wrote was the times and dates of some previous banging noises and asked that they stop. about 2 days later we had another letter from her stating that she is definatly smelling our cigarette smoke and that the banging is happening when she smells us smoking. SO, I have talked to the property manager, she is fed up with the psycho, I have emailed HER boss twice with no response. I can't catch the banging on camera because it is at the most random times. I don't want to get the police involved only because having been raised by a cop I know they have better **** to do with their time than knock on doors and smell for cigarettes. Even if I do call them she will probably make up some B S story about how it is all in our heads and we smoke (Crazy people can make up some really believable stories when they need to, I dated a few...) (j/k) Does anyone have similar experiences, how did you deal with it, or does anybody have any suggestions on how I should move forward? Thank you for you reading!