lots of rules, no wiggle room
Sorry it's taken me so long to reply. I don't have an internet computer at home, and I have a disability which sometimes prevents me from getting out of the house, so my access to the internet depends on my ability to get to the library.
The gist of NH laws are thus (and I could cut & paste my e-mails to and from the NH DMV in Concord if necessary): in NH, any bicycle with a gas-powered motor attached must be registered either as a moped or as a motorcycle in order for that vehicle to be road legal.
It is generally easier and less expensive to register one's motorized bicycle as a moped but it must fall into the following strict category: the engine must be 2hp or less, the cc's must be 50 or less, and (here's the catch) the maximum operational speed attained in one mile must be 30 mph or less. If any one of these does not conform (such as the speed ) it must then be registered as a motorcycle.
As for the speed, it is not sufficient that the operator of the motorized bicycle voluntarilly keep the speed below 30 mph. Rather, 30 mph must be the top speed the engine is able to produce in one mile. I realize many factors can influence the max operational speed, and the NH DMV was a real stickler on this point. "The rules are the rules" seemed to be their attitude despite my pointing out the fact that many variables can influence an engine's max op speed (weight of rider, tire rolling resistance, wind direction, wind speed, whether or not your elbows are tucked in, weight of groceries in backpack, etc.).
Oh, and if upon registration you don't provide documentation from the engine manufacturer as to the expected max op speed, the NH DMV will do research, I was informed, in order to determine that speed. And before you go to register your motorized bicycle as a moped you must first get a VIN # for it from the NH State Police for $30 (there's a number you can call to reach the Troopers about getting a VIN).
It all seems absurd, like we're trying to get away with stealing a nuclear weapon or something. I mean, really, it's just a bicycle with a weed whacker engine on it, why all the strick legal codes?
The fee, I believe, for getting pulled over by the cops without a registration: $100.