I think counterrevolutionary crime is the thing to worry about more than petty crime. To do that, you have to start from the top and move down.

Quietly get rid of the intelligence agencies and top military commanders. Replace military with politically aligned revolutionaries. This cripples the creation of new operations against you. Now you have to deal with existing ops that can easily operate without a head. This means going after organized crime. Go after the big drug dealers, the human traffickers, black market goods, etc. You also have to go after the legitimate face of intelligence, all the companies used as fronts for operations. That means nationalizing energy, pharmaceuticals, weapons, banking. Go after the money next, cut everyone off from their off-shore banks and hiding places.

The national level will have to deal with the big stuff and then you can have community defense cover petty/local/individual crime. There has to be some national directive there though because counterrevolutionary violence will be carried out at the local level.

That'll keep you busy for a while. Once that's done you can bring in a restorative justice system and probably have eliminated most crime.