Every bicycle with a motor attached is defined as a motor-driven cycle.
The operation of a motor-driven cycle requires a class M driver license. Restricted class M driver licenses are available for those as young as 14 years of age. Arizona
Under Arizona law, motorized electric bicycles and tricycles meeting the definition under the applicable statute are not subject to title, licensing, insurance, or registration requirements, and may be used upon any roadway authorized for use by conventional bicycles,
including use in bike lanes integrated with motor vehicle roadways. Unless specifically prohibited, electric bicycles may be operated on multi-use trails designated for hiking, biking, equestrian, or other non-motorized usage, and upon paths designated for the exclusive use of bicycles. No operator's license is required, but anyone operating a bicycle on Arizona roads must carry proof of identity.
A "motorized electric bicycle or tricycle" is legally defined as a bicycle or tricycle that is equipped with a helper motor that may be self-propelled, which is operated at speeds of less than twenty miles per hour. Electric bicycles operated at speeds of twenty miles an hour or more, but less than twenty-five miles per hour may be registered for legal use on the roadways as mopeds, and above twenty-five miles per hour as a registered moped with an 'M' endorsement on the operator's driving license. However, mopeds in Arizona are prohibited from using bike lanes on motor vehicle roadways. The Arizona statute governing motorized electric bicycles does not prohibit local jurisdictions from adopting an ordinance that further regulates or prohibits the operation of motorized electric bicycles or tricycles. Arkansas
Arkansas does not define E-bikes. The following definition describes a combustion engine. E-bikes being electric do not have a cylinder capacity and thus this law is not technically applicable. The state defines a "Motorized bicycle" as "a bicycle with an automatic transmission and a motor of less than 50cc."
Riders require either a certificate to operate a motorized bicycle, a motorcycle license, a motor-driven cycle license, or a license of class A, B, C or D. Certificates cannot be issued to riders under 10 years of age. California
Electric Bicycles are defined by the California Vehicle Code.
New legislation became effective January 2016. The current regulations define an "electric bicycle": a bicycle equipped with fully operable pedals and an electric motor of less than 750 watts, separated into three classes: A "class 1 electric bicycle," or "low-speed pedal-assisted electric bicycle," is a bicycle equipped with a motor that provides assistance only when the rider is pedaling, and that ceases to provide assistance when the bicycle reaches the speed of 20 miles per hour. (2) A "class 2 electric bicycle," or "low-speed throttle-assisted electric bicycle," is a bicycle equipped with a motor that may be used exclusively to propel the bicycle, and that is not capable of providing assistance when the bicycle reaches the speed of 20 miles per hour. A "class 3 electric bicycle," or "speed pedal-assisted electric bicycle," is a bicycle equipped with a motor that provides assistance only when the rider is pedaling, (no throttle) and that ceases to provide assistance when the bicycle reaches the speed of 28 miles per hour, and equipped with a speedometer. Local government ordinances are allowed to permit or ban any class of electric bicycles on dedicated bicycle paths and trails, with Class 1 & 2 permitted, and Class 3 banned, by default. Beginning January 1, 2017, manufacturers and distributors of electric bicycles will be required to apply a label that is permanently affixed, in a prominent location, to each electric bicycle, indicating its class. Should a user "tamper with or modify" an electric bicycle, changing the speed capability, they must replace the label indicating the classification.
Driver's licenses, registration, insurance and license plate requirements do not apply. An electric bicycle is not a motor vehicle. Drinking and driving laws apply. Additional laws or ordinances may apply to the use of electric bicycles by each city or county. Colorado
Ebike definition in Colorado follows the HR 727 National Law: 20 mph (30 km/h) e-power and 750 W (1 hp) max, 2 or 3 wheels, pedals that work. Legal low-powered ebikes are allowed on roads and bike lanes, and prohibited from using their motors on bike and pedestrian paths, unless overridden by local ordinance. The city of Boulder is the first to have done so, banning ebikes over 400W from bike lanes. Bicycles and Ebikes are disallowed on certain high speed highways and all Interstates unless signed as "Allowed" in certain rural Interstate stretches where the Interstate is the ONLY means of travel. Connecticut
Section 14-1 of Connecticut state law classifies electric bicycles as "motor-driven cycles" if they have a seat height of not less than 26 inches and a motor which produces brake horsepower of 5 or less.
Motor-driven cycles may be operated on the roadway without registration, but the operator must have a driver's license.
The cycle may not be operated on any sidewalk, limited access highway or turnpike. If the maximum speed of the cycle is less than the speed limit of the road, the cycle must operate in the right hand lane available for traffic or upon a usable shoulder on the right side of the road unless the operator is making a left turn. District of Columbia
Electric-assist and other "motorized bicycles"
do not need to be inspected, do not require a license, and do not require registration. The vehicle must meet all of the following criteria: a post mounted seat for each person it is designed to carry, two or three wheels which contact the ground, fully operative pedals, wheels at least 16 inches in diameter and a motor not capable of propelling the device at more than 20 mph on level ground. The driver does not need a license, but must be at least 16 years old. DC law prohibits motorized bicycles from traveling anywhere on the sidewalk or in the bike lanes. DC Regulation 18-1201.18 provides: "Except as otherwise permitted for a motor vehicle, no person shall operate a motorized bicycle on any sidewalk or any off-street bikepath or bicycle route within the District. This prohibition shall apply even though the motorized bicycle is being operated solely by human power." So, if cars are prohibited in a particular place, motor-assisted bikes are also prohibited. Florida
Florida DMV Procedure RS-61 II. "(B.) Dirt bikes noted for off road use, motorized bicycles and Go-Peds are not registered."  Electric Helper-Motor Bicycles
If you are at least 16 years old, a person may ride a bicycle that is propelled by a combination of human power (pedals) and an electric helper-motor that cannot go faster than 20 mph on level ground without a driver license. Motorized Bicycles and Motorized Scooters
Under Title 23, Chapter 316 of the code, bicycles and motorized bicycles are defined as follows: Bicycle
—Every vehicle propelled solely by human power, and every motorized bicycle propelled by a combination of human power and an electric helper motor capable of propelling the vehicle at a speed of not more than 20 miles per hour on level ground upon which any person may ride, having two tandem wheels, and including any device generally recognized as a bicycle though equipped with two front or two rear wheels. The term does not include such a vehicle with a seat height of no more than 25 inches from the ground when the seat is adjusted to its highest position or a scooter or similar device. No person under the age of 16 may operate or ride upon a motorized bicycle. Motorized Scooter
—Any vehicle not having a seat or saddle for the use of the rider, designed to travel on not more than three wheels, and not capable of propelling the vehicle at a speed greater than 30 miles per hour on level ground.
In addition to the statutory language, there are several judicial rulings on the subject. Georgia
Georgia Code 40-1-1 Part 15.5 (15.5) 'Electric assisted bicycle' means a device with two or three wheels which has a saddle and fully operative pedals for human propulsion and also has an electric motor. For such a device to be considered an electric assisted bicycle, it shall meet the requirements of the Federal Motor Vehicle Safety Standards, as set forth in 49 C.F.R. Section 571, et seq., and shall operate in such a manner that the electric motor disengages or ceases to function when the brakes are applied. The electric motor in an electric assisted bicycle shall:
(A) Have a power output of not more than 1,000 watts;
(B) Be incapable of propelling the device at a speed of more than 20 miles per hour on level ground; and
(C) Be incapable of further increasing the speed of the device when human power alone is used to propel the device at or more than 20 miles per hour. Hawaii
A Federal agency, the Consumer Product Safety Commission (CPSC), has exclusive jurisdiction over electric bicycles as to consumer product regulations, but this does not change state regulation of the use of electric bicycles on streets and highways.
means every vehicle "propelled solely by human power" upon which any person may ride, having two tandem wheels, and including any vehicle generally recognized as a bicycle though equipped with two front or two rear wheels except a toy bicycle. 
"Moped" means a device upon which a person may ride which is DOT Approved.
Under the statute, mopeds must be registered. To be registered under Hawaii law a moped must bear a certification label from the manufacturer stating that it complies with federal motor vehicle safety standards (FMVSS). A moped must also possess the following equipment approved by the D.O.T. under Chapter 91: approved braking, fuel, and exhaust system components; approved steering system and handlebars; wheel rims; fenders; a guard or protective covering for drive belts, chains and rotating components; seat or saddle; lamps and reflectors; equipment controls; speedometer; retracting support stand; horn; and identification markings. Illinois (625 ILCS 5/11‑1516)
Sec. 11‑1516. Low‑speed bicycles.
(a) A person may operate a low‑speed electric bicycle or low‑speed gas bicycle only if the person is at least 16 years of age.
(b) A person may not operate a low‑speed electric bicycle or low‑speed gas bicycle at a speed greater than 20 miles per hour upon any highway, street, or roadway.
(c) A person may not operate a low‑speed electric bicycle or low‑speed gas bicycle on a sidewalk.
(d) Except as otherwise provided in this Section, the provisions of this Article XV that apply to bicycles also apply to low‑speed electric bicycles and low‑speed gas bicycles.
(Source: P.A. 96‑125, eff. 1‑1‑10.)
A motorized pedalcycle requires a driver's license and is limited to 2 horsepower and 30 MPH over a 1-mile stretch.