Shocking, I know. But until recently, there was no statisticly significant evidence that police actually reduce crime. Generally, cities with more crime have more police. That fact makes it hard to tell if police reduce crime. In order to tell if police levels actually reduce crime, you need to remove the cause and effect. In other words, you need to find a period of time when police levels are increased for some reason other than increased crime. And that doesn't happen often. But 9/11 provided that. With the new terror alerts, some cities increased their police presence because the government terror alert went to Orange. In particular, Washington D.C. did. Alex Tabarrok went and studied crime rates when the alert level was Yellow (less police) and when it was Orange (more police). His study suggests that increasing police presence by 10% reduces crime by 4%. Because of the costs of each (crime is costlier than police) it's probably cost effective to start bumping up police presence significantly.
Paper can be found: http://mason.gmu.edu/~atabarro/TerrorAlertProofs.pdf