police assault woman, charge her with a crime that never happened.

[WEB slicer]

then they delete the video evidence.

http://www.cnn.com/video/data/2.0/video/crime/2014/12/11/lv-dnt-baltimore-police-brutality-video.wjz.html

[Snorek]

I have one question. You can or cannot record Police at work? I always thought that you can. Care to enlighten me?

[Balthazar]

You can but they'll spend some time to explain you why you can't.

[donseptico]

I have one question. You can or cannot record Police at work? I always thought that you can. Care to enlighten me?

Depends where you live but here in the UK yeah sure... although they'll probably not like it and try to persuade you to stop: Freedom to photograph and film
Members of the public and the media do not need a permit to film or photograph in public places and police have no power to stop them filming or photographing incidents or police personnel.