These are Federal regulations that put control of monitoring the safety of electric bicycles into the hands of the Consumer Products Safety Commission (CPSC), which supersede any state law that is more stringent, but only regarding safety equipment required on electric bicycles and not regarding whether electric bicycles are street legal. The states still decide what vehicles are allowed to use the roads in their state.
U.S. Department of Energy reports that “Since [1998, when federal rules
regulating equipment on these vehicles became effective], 37 states
have passed legislation allowing these vehicles to be driven on roads
with posted speed limits of 35 miles per hour or lower.” 
TEA-21 and SAFETEA-LU Specify that legal Ebikes, as defined above, are legal on urban bicycle trail systems getting any federal funding unless states or local entities have passed laws specifically dis-allowing electric assist bicycles. Under Federal Law, Ebikes are NOT considered motor vehicles unless the state or local entity has passed a law otherwise.
There is a MISCONCEPTION that when "motor vehicles" or "motorized vehicles" are disallowed by law or by signage, that this always means ebikes are illegal on trails. This is UNTRUE in many states; these terms do not include "legal low power electric assist bicycles", and can only be banned by passing a specific state or local law. (See TEA-21 Federal DOT Law)
SAFETEA-LU is a 2005 Federal Re-authorization of the 1990s TEA-21, and renews the exclusion of legal ebikes from the classification of 'motor vehicles' from urban trail use unless a specific local ebike statute is passed.
"Motorized vehicles are not permitted on trails and pedestrian walkways EXCEPT FOR: maintenance purposes, motorized wheelchairs, and—when State or local regulations permit—snowmobiles and electric bicycles. Electric bicycles are defined for the purposes of this Act as a bicycle or tricycle with a low-powered electric motor weighing less than 100 pounds with a top motor-powered speed not in excess of 20 miles per hour."
Safe, Accountable, Flexible, Efficient Transportation Equity Act: A
Legacy for Users, P.L.109-59 Available from the Government Printing
Office or online at www.dot.gov. Title 23,
There is some debate as to if and where the 100 lb rule applies. On the surface it appears to be valid on trails. Check your state and local laws for any recent changes.
As always, unsafe operation may be a specific illegal or civil matter to be handled by local courts.
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