Trust me, crime is plentiful in NH. I witness someone committing a crime that's semi major on a daily basis. There isn't the police force up here to enforce it. There's a huge opium problem in the state, and no one ever gets arrested because there's no cops. And when cops catch someone doing something illegal it's usually petty enough to be let off.
For example, a coworker of mine went 2 years without getting his car registered or inspected. In NJ I forgot when mine was due and was caught in 8 days. He went 2 years. Think about that.
There's always going to be crime even in the whitest communities. You'll have your assaults, drug possessions, thefts, dui's, domestic batteries etc but I'm referring to the lack of aggravated felonies which you won't have. There are more murders in a week in Chicago than New Hampshire has a year.