I would think that electric assisted biking would be covered by the laws for vehicles, not human powered bicycles. Is that not correct?
Class 1 bikes only assist when the rider pedals. They make sustaining speeds and climbing hills easier. They are generally allowed wherever bikers are, and have speed limiters.
Class 2 bikes use a throttle, and do not require peddling, and are generally considered a motorized vehicle.
Class 3 bikes are fuzzier. They operate like class 1 bikes (pedal to get power) but they can get motor assistance up to 28 mph. These bikes are generally allowed to operate like class 1 bikes as long as they stay under 20mph, but may be banned from some mixed use areas.
I've been a cyclist in many cities. Never once seen a cop cite someone for this. I'm guessing if you got into a bad accident things would go poorly for you after it was discovered what you did, but has anyone here actually seen something come of people riding these bikes where they are banned?
It's great to have for residential streets though, because I can generally sustain the 25 mph that cars do AND can treat stops as yields.