HI @atherz, great question!
These societies are meant to exist alongside and within current governmental models. An ON would pay taxes to the state or country which it resides and have access to its police services as any other citizen would (this is a last resort).
However, I would imagine there would be less crime, as crime is motivated by a lack of needs being met. ON is designed to better meet our needs, hence reduce crime. Further, when we have access to all we need, we don't need to steal to obtain said access.
When we are in a supporting and collaborative environment, mental illness has a chance to heal.
Finally, long before involving state agencies (police) there is dispute resolution built into ON that gives members a structured process of dealing with conflict- and a gradient scale for handling and healing conflict (crime).