Most citizens are concerned with rising crime rates, and many of them want a say in a solution. Many, however, do not necessarily want to be involved in the solution. For some, they don't feel as if their input will be significant enough to make a difference. For proof of this, look at the number of people who don't vote. Apathy and a lack of feeling empowered would lead to this lack of activism too.
My opinion is that most citizens are very concerned with crime in the neighborhoods that they live in. Unfortunately, sometimes it takes burglaries or other crimes in the neighborhood before people become concerned about it though. I do believe that people need to work together in order be successful and aggressive in stopping crime.
I would have to say that for the most part most citizens want to at least have a voice in how to prevent crime in their own neighborhood. The level of involvement beyond that I believe will depend on factors such as gender and age.
With the increasing lack of protection afforded by local governments, citizens have begun to "take matters into their own hands." For example, Citizens' Watch and Neighborhood Watch have been created for this reason; in another example there is a volunteer group of men who walk the neighborhoods and areas of high crime and help protect law-abiding citizens.
Having lived in several different neighborhoods in my adult life, my answer is that it largely depends on the neighborhood. And, from my experience, socio-economic status is a big factor in the citizen-willingness to do anything on a volunteer basis.
Consider the fact that stay-at-home moms, for example, have a more directly vested interest and more time on their hands when it comes to community matters. People who are not parents, single mothers who have to work, or even married couples who both have careers, may not have the time nor the energy for volunteering in community programs, including crime-prevention.
On the other hand, citizens who have been directly affected by specific crimes, often hit the point where they will sacrifice in order to join a cause in preventing it further. In these kinds of cases, I think even the busiest of citizens create time to contribute to causes they feel are worthy.
The answer to this depends upon a number of issues, but citizens generally do want to be at least somewhat involved in the prevention of crime in their own neighborhoods.
Citizens generally want to have the authorities pay attention to them. They want the authorities to listen to what they have to say in terms of what crimes should be the highest priority and how they should be prevented. If their wants are heeded, they will be more interested in being involved in crime prevention.
If, on the other hand, the crime prevention strategies proposed by police seem too instrusive, or if they are not aimed at the "right" things, citizens will be much less supportive of those efforts.
So the nature of the crime prevention tactics is one factor that determines how interested citizens will be in crime prevention in their neighborhoods.