The only neighborhood watch programs I've seen in my community emphasize being alert and reporting suspicious persons. A Police officer will meet with people and tell them what to be alert for. No patrols involved.
And of course, citizens have banded together to protect their neigborhoods during times of unrest brought about by natural, as well as man made, events. As LE availability decreases, criminal activity increases.
As far as citizen patrols are concerned, I believe Dave is correct with re: to carrying firearms. To be sanctioned by the Police, you'd have to agree to that.
Maybe one of the good things about armed citizens patrolling their neighborhoods without approval is that it, alone, would tend to bring out the Police faster than a cop can down a doughnut--- if only to keep an eye on the armed citizens while giving the thugs even more incentive to disappear.
To get the ball rolling, a simple call to your local Sheriff or PD non emergency number should do the trick. If you get stonewalled, and you have a serious situation in your neighborhood, the other call you make is to your local media. All of them.
You may have to put the Police in the spotlight to get results. They may not even have a Police sanctioned citizen patrol program. They may be short on manpower. Might mean some work involved and the co-operation of lots of neighbors--not just a few.
You have to weigh the size of the problem in relation to the work involved in solving it.