I had been told that in Texas, an electric bike was considered a motorized vehicle and you had to get registration and insurance and pass a motorcycle test. After some research, I found that that really wasn’t the case. The problem is, that most police officers don’t know the laws (such as the person who told me about ebikes) and you might get stopped. Being courteous and informed can go a long way to promoting the use of these great bikes.
The US Federal government passed a law, Public Law 107-319, saying that an ebike, electric bicycle, is a bicycle and not a motor vehicle as long as the motor is under 750 watts, with operating pedals and limited to 20 mph. This would supersede any state law although states can certainly add laws. My state of Texas says that electric bikes are defined in the Transportation Code Title 7, Chapter 551 entitled "Operation of Bicycles, Mopeds, and Play Vehicles" in Subchapter A, B, C, and D. Under Chapter 541.201 (24), "Electric bicycle" means a bicycle that is (A) designed to be propelled by an electric motor, exclusively or in combination with the application of human power, (B) cannot attain a speed of more than 20 miles per hour without the application of human power, and (C) does not exceed a weight of 100 pounds. The department or a local authority may not prohibit the use of an electric bicycle on a highway that is used primarily by motor vehicles. The department or a local authority may prohibit the use of an electric bicycle on a highway used primarily by pedestrians.
Most states do have safety laws pertaining to bicycles so you still have to follow the rules of the road for bikes.