Although the US doesn't usually show that kind of footage on purpose, sometimes it happens on live TV. I think it may happen semi-often in California in particular due to the live car chases. I'm not sure, but I think there may have been some kind of law passed after a particularly brutal occurance. I think there is always some kind of delay involved in televised car chases now just-in-case.
I remember one in particular when I was younger-- where a man stole a tank and went on a rampage with it. Here's the article on wikipedia:
Shawn Nelson - Wikipedia, the free encyclopedia
I remember a few more, but extremely vaguely... I think I remember seeing one where there was a shotgun involved.