It seems that I remember a kidnapping case that was bogus and the cost of the investigation was charged back to the perpetrators but the details elude me to the point I can't even find it on google. I may have imagined it.
At one time, our city charged for burglar alarms they had to respond to more than twice in one month if the alarm was unfounded. It took several months but the faulty alarms that were going off multiple times a day were eventually fixed. I'm not sure they charge for false alarms any more though. (And yeah, I realize that isn't the same thing, but my mind wandered off.)