Yes, absolutely you may request the video. Don't be surprised if "the camera wasn't working" or "there was a malfunction". Unless, of course, the video is incriminating.
It is always in your best interest to retain experienced counsel to assist you in such cases.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.