Not true- other way around if there is a true conflict between the laws.
However, in practice what happens is that unless the federal law, or state law states that it preempts other law or is regulating in an arena that gives that level of government exclusive authority, a more strict law can be enforced by a smaller governmental unit. Then the more strict rule applies.
Here is an illustration. If a state law said this: "Bicycles with engines at 2hp or below which do not exceed 25 mph may be operated without registration", but a local law stated: "bicycles cannot be operated on the roads in the village of Squaresville." The more strict law applies because the state law only speaks to registration and does not state that towns cannot make other limitations. Clearly, however, towns could not require registration.
However, states may pass laws that state something like: "Bicycles with engines at 2hp or below which do not exceed 25 mph may be operated on the roads of this state." Then a local givernment cannot conflict with that law and any local law which purports to conflict with it is invalid. Local laws could not say the motorized bicycle cannot operate on their streets because the state already says they can. The is an implication that local laws are preempted. Beware, however, that there may be a statement, either in the same statute or in another that says: "Notwithstanding any provision....municipalities may regulate the use of motorized bicycles within their limits." That is the state giving power to the local government, not being overridden by the local law.
As for the federal laws above...I am getting a little tired of the misinformation all over the place. All those laws have to do with is the manufacturing standards the item must meet to be imported or sold. They do not make anything legal or illegal for use on any road anywhere. That is not the purpose of those regulations
Individual states may choose to reference those regulations in defining what can operate on their roads, but they are under no obligation to do so. Definition of what vehicles may operate intrastate (as opposed to interstate) is a state law issue. There is some doubt as to whether it would even be Constitutional for the federal government to make a law the instructed that motorized bicycle would be legal to operate anywhere across the country.
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1998 law school graduate
Member of the state bar of Indiana since 1998
Admitted to practice in several federal courts since 1998
Undergraduate and law school adjunct Professor of Law since 2004
Motorbiker since 2007