Effective July 1, 2015, "mopeds" must be registered with DMV to operate on roadways.
A moped is "[a] vehicle that has two or three wheels, no external shifting device, and a motor that does not exceed 50 cubic centimeters piston displacement and cannot propel the vehicle at a speed greater than 30 miles per hour on a level surface" according to NCGS 20-4.01
Insurance is not yet required but that may change in the future.
Failing to register a moped is a Class 3 misdemeanor, as is allowing your moped to be driven on the roads by someone else without registering it. So if your ne'er do well buddy takes your unregistered moped for a spin in the nearby parking lot, you can get a criminal record, just as you can get a criminal record if you drive the moped on the street.
It is also an offense to fail to display a current registration plate on a moped.
The statute includes public vehicular areas, which for all intents and purposes is how parking lots and the like are defined in the law.