The whole point of community policing is crime prevention as opposed to apprehending suspects once a crime has occurred. Police and community members are supposed to work together to figure out ways to reduce crime in any given area.
In my town, perhaps the most important problem that could be addressed by community policing is gang activity. This is a problem that might be addressed by a combination of after-school programs and of police foot or bike patrols where police would become familiar with all the people in a given area. This might allow them to put constant pressure on youths to stay away from gang activity.
A second problem that could be addressed, though this would be harder to manage, would be residential burglaries. If the police could help to set up and organize neighborhood watch programs, they might be able to give people in the neighborhoods practical tips for how to help prevent burglaries of their own homes and their neighbors' homes.
Community policing is best at addressing these sorts of relatively minor crimes that can degrade a neighborhood's quality of life and perhaps lead to more serious problems.