That's why some jurisdictions implement "guilty until proven innocent" against their police force, making turning off the camera (or "not noticing it just broke") and proceeding to beat someone up a rather bad idea.
There should at least be a bias against the officer's word from the judge and the jury if he intentionally stopped the camera from filming before a police action.
As it is, cops already get the benefit of the doubt almost all the time and when they don't deserve it.
My Ukrainian friend claimed it's the case with the new police force. They are extremely careful about turning those cams on before approaching anyone, even when they're helping an old lady through the street. I can't read the language to get primary sources myself, googling for English texts gave me only stories on how the judiciary system (not replaced) there is practically at war with the police (effectively rebuilt from ground after the last revolution).
Sadly, I can't see any western country doing it yet. Damn, in my home country there was a case of assault against police officer. A video got public showing the officer walking up to the guy, throwing him on the ground and proceeding to kick him. I believe the judge still took the cop's word.
The thing in Ukraine also has ridiculously tough responsibility for body injuries.
I can't comment on specific laws concerning police, but can on self-defense. Basically if someone tries to rob you and you break robbers arm you can be hold criminally liable.
This comes as a Soviet legacy, there's some push to change the laws in question.
As it is, cops already get the benefit of the doubt almost all the time and when they don't deserve it.