Well, in the Texas Vehicle Code there's this:
Sec. 542.202. POWERS OF LOCAL AUTHORITIES. (a) This subtitle does not prevent a local authority, with respect to a highway under its jurisdiction and in the reasonable exercise of the police power, from:
(4) regulating the operation and requiring registration and licensing of a bicycle or electric bicycle , including payment of a registration fee, except as provided by Section 551.106;
Section 551.106 says this:
Sec. 551.106. REGULATION OF ELECTRIC BICYCLES. (a) 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.
(b) The department shall establish rules for the administration of this section.
So, it would seem that a local authority can force you off the road on a bicycle, but NOT if it is an electric bicycle!
Speedo