Have you done any searching at NJ's laws website? Normally, the people in the state where they reside will look 'em up, and report back.
A two minute google search brought me here - it looks like you could find some information under Title 39...
BTW. The section you're interested in is 39:4-14.3
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++ A synopsis based on my reading of NJ statues:
MBs must be registered (cost is $8 a year,) and liability insurance is required.
Operators may not be younger than 15. Operators must possess either a drivers license of any class or a motorized bicycle drivers license. A motorized bicycle learners permit can be issued.
A motorized bicycle is defined as follows: "Motorized bicycle" means a pedal bicycle having a helper motor characterized in that either the maximum piston displacement is less than 50 cc. or said motor is rated at no more than 1.5 brake horsepower or is powered by an electric drive motor and said bicycle is capable of a maximum speed of no more than 25 miles per hour on a flat surface.
Motorized bicycles not allowed on interstates or divided highways, or on highways with posted speed limits greater than 50 MPH... MBs CAN be prohibited from roads/highways with speeds greater than 40MPH if it's determined that this road is dangerous to motorized bicycles.
MB's shall be operated under laws/regulations of bicycles (39:4-14,) unless otherwise noted.
MB's get Moped plates.
Interestingly, repricosity (sp) is observed with other states, so, if you are a resident of another state, so long as you operate the bike in accordance with your home state laws, then you're OK with New Jersey.
A helmet is required.
Reflective tire sidewalls are required! Plus a plethora of other reflectors, (Plus, lights, and a bell, from bicycle ordinances.)
First offense - warning. Second offense - fine of $10. third and subsequent offenses, fine of not more than $100, bus impoundment of bike up to 30 days.
Note that I am not a lawyer, (nor would I want to be one,) so if you want to be sure that you're operating under the laws of NJ, you should probably talk to a lawyer, and/or the police.
There's a few issues with this law. First is the non-operation on highways with speed limits over 50 mph. That excludes a good part of the rural areas of the state. Second, apparently trikes aren't covered under the laws, nor are recumbent bikes.