Motorized bicycle

The legal status of an ICE motorized bicycle in the United States is presently determined by the laws of each state and/or local jurisdiction. Several states allow ICE motorbikes to be operated on roadways without registration, tax, or licensing in the same manner as bicycles, providing certain restrictions are observed. Many state jurisdictions use limits on top speed and/or engine displacement to determine if ICE motorized bicycles require registration and licensing--sometimes as mopeds, sometimes as motorcycles. Some states prohibit the use of motorbikes on multi-use recreational paths or high-speed, limited access roadways, while others require additional safety equipment for operation on public roads, such as wearing a helmet. Many United States cities and other local jurisdictions may impose additional restrictions upon ICE motorized bicycles when operated on public streets and roadways.

Is this statement correct "is it illegal to put an engine on a bicycle"?
no