Old thread, but here is the official Texas law concerning motor assisted bicycles/scooters:
http://www.statutes.legis.state.tx.us/docs/tn/htm/tn.551.htm
SUBCHAPTER E.  MOTOR-ASSISTED SCOOTERS
Sec. 551.351.  DEFINITIONS.  In this subchapter:
(1)  "Motor-assisted scooter":
(A) means a self-propelled device with:
(i)  at least two wheels in contact with the ground during operation;
(ii)  a braking system capable of stopping the device under typical operating conditions;
(iii)  a gas or electric motor not exceeding 40 cubic centimeters;
(iv)  a deck designed to allow a person to stand or sit while operating the device; and
(v)  the ability to be propelled by human power alone; and
(B)  does not include a pocket bike or a minimotorbike.
(2)  "Pocket bike or minimotorbike" means a self-propelled vehicle that is equipped with an electric motor or internal combustion engine having a piston displacement of less than 50 cubic centimeters, is designed to propel itself with not more than two wheels in contact with the ground, has a seat or saddle for the use of the operator, is not designed for use on a highway, and is ineligible for a certificate of title under Chapter 501.  The term does not include:
(A)  a moped or motorcycle;
(B)  an electric bicycle or motor-driven cycle, as defined by Section 541.201;
(C)  a motorized mobility device, as defined by Section 542.009;
(D)  an electric personal assistive mobility device, as defined by Section 551.201; or
(E)  a neighborhood electric vehicle, as defined by Section 551.301.
Added by Acts 2005, 79th Leg., Ch. 1242, Sec. 3, eff. June 18, 2005.
Amended by: 
Acts 2011, 82nd Leg., R.S., Ch. 91, Sec. 24.015, eff. September 1, 2011.
Sec. 551.352.  OPERATION ON ROADWAYS OR SIDEWALKS.  (a)  A motor-assisted scooter may be operated only on a street or highway for which the posted speed limit is 35 miles per hour or less.  The motor-assisted scooter may cross a road or street at an intersection where the road or street has a posted speed limit of more than 35 miles per hour.
(b)  A county or municipality may prohibit the operation of a motor-assisted scooter on a street, highway, or sidewalk if the governing body of the county or municipality determines that the prohibition is necessary in the interest of safety.

  The department may prohibit the operation of a motor-assisted scooter on a highway if it determines that the prohibition is necessary in the interest of safety.
(d)  A person may operate a motor-assisted scooter on a path set aside for the exclusive operation of bicycles or on a sidewalk.  Except as otherwise provided by this section, a provision of this title applicable to the operation of a bicycle applies to the operation of a motor-assisted scooter.
(e)  A provision of this title applicable to a motor vehicle does not apply to a motor-assisted scooter.