Yes. Thus why you now need to enhance your Investigative efforts. There's a thread in the Strategy and Tips section here: http://forums.civfanatics.com/showthread.php?t=561705 More information is given on fighting criminals in the city if you scroll down some posts from the first one.
As I understand, a dog or other unit with police ability sees the crime 1-3 fields before its position and can fight it then. But a crime being in city it can't attack, but If I remember right, I found a workaround past time (not yet tried it again):
If you see a crime in your city, remove all units off it. The cimes are the remaining, and then attack the city by police (or a sniper or another special unit?), and the cimes are dead. (maybe little different and not possible with all units, but something like that I believe to remember)