A quick search turned up it's a county thing to resister the bicycle. This one here is for Harris County in particular:
Sec. 45-311. Required.
(a) It shall be unlawful for any person to operate a bicycle wholly or in part by muscular power within the city unless such bicycles is registered with the city as provided in this division.
(b) Any person operating a bicycle which is owned by a nonresident of the city and which is currently licensed pursuant to the requirements of any other Texas municipality shall be exempt from subsection (a).
(c) The term "operate" as used in this section shall mean to ride, walk with, park, stand, or be in possession of; excluded from the meaning of this term shall be in the possession of bicycles held for sale by one who engages in the business of the retail or wholesale sale of bicycles.
(Code 1968, § 46-289; Ord. No. 72-1598, § 1(1), 9-6-72)
Sec. 45-312. Administration.
The police department shall administer the provisions of this division except where hereinafter otherwise provided. The police chief or his authorized agent shall issue consecutively numbered books of bicycle licenses to the fire chief or his authorized agent. The officer in charge of each fire station shall be responsible for registration, issuance of licenses or decals and the collection of moneys as provided for in this division.
(Code 1968, § 46-290; Ord. No. 72-1598, § 1(2), 9-6-72)
Sec. 45-313. Procedures, fees, etc.
Bicycles shall be registered at any fire station in the city pursuant to the following terms, conditions and requirements:
(1) The bicycle shall be brought to the fire station.
(2) A registration form provided by the city shall be filled out and signed by the owner of the bicycle.
(3) A registration fee of $1.00 shall be paid in advance.
(4) As evidence of the completion of the above paragraphs, the city shall provide a decal or license plate which shall be permanently affixed to the bicycle according to specifications established by the police department. The city shall also furnish the owner with a registration card.
(Code 1968, § 46-291; Ord. No. 72-1598, § 1(3), 9-6-72)
Sec. 45-314. Registration to be permanent until change of ownership.
The registration of a bicycle shall be permanent so long as the ownership thereof remains in the person registering the bicycle. Upon any change of ownership, the bicycle shall be registered in the name of the new owner in accordance with the requirements of this division.
(Code 1968, § 46-292; Ord. No. 72-1598, § 1(4), 9-6-72; Ord. No. 74-1732, § 1, 10-1-74)
Sec. 45-315. Removal, destruction, etc. of manufacturer's serial number, license plate or license decal.
It shall be unlawful for any person to willfully or maliciously remove, destroy, deface or alter the manufacturer's serial number on the frame of any bicycle, or the license plate or license decal applied or attached to any bicycle registered under this division, while such plate or decal is valid. Violation of this section shall be punished as provided by section 1-6 of this Code.
(Code 1968, § 46-293; Ord. No. 72-1598, § 1(5), 9-6-72; Ord. No. 92-1449, § 63, 11-4-92)
Charter references: Penalty for ordinance violation, Art. II, § 12.
Cross references: Assessment of fines against corporations, § 16-76; payment of fines, § 16-78; credit against fines for incarceration, § 35-6 et seq.
Sec. 45-316. Sale or transfer of ownership of bicycle.
It shall be the duty of any person who sells or transfers ownership of any bicycle registered under this division to report such sale or transfer, within ten days thereof, to the police department of the city by returning the registration card together with the name and address of the person to whom the bicycle was sold or transferred. It shall be the duty of the purchaser or transferee of any bicycle to register same according to the provisions of section 45-313 of this Code, within 20 days of the sale or transfer.
(Code 1968, § 46-294; Ord. No. 72-1598, § 1(6), 9-6-72)
Sec. 45-317. Reports of bicycles permanently removed from operation.
Within ten days after any bicycle licensed under this division shall have been dismantled, destroyed or otherwise permanently removed from operation, such information shall be reported to the police department by the person in whose name the bicycle was last registered.
(Code 1968, § 46-295; Ord. No. 72-1598, § 1(7), 9-6-72)
Sec. 45-318. Monthly reports of dealers.
Every person engaged in the business of buying, selling, trading or otherwise exchanging new or used bicycle or bicycle frames shall make a monthly report to the chief of police of every bicycle or bicycle frame bought, sold, or otherwise acquired or transferred, giving the name and address of the person from whom acquired or to whom transferred, a description of such bicycle or bicycle frame by name or make, the manufacturer's serial number and the license number, if any, found thereon. Any violation of this section shall be punished as provided by section 1-6 of this Code.
Sec. 45-319. Responsibility of parents or guardians; penalty.
It shall be unlawful for any person to commit, or for the parent or guardian of any minor to knowingly allow or permit their child or ward to commit any act forbidden by this division or to fail to do any act required by this division. Unless expressly provided otherwise in this division, a violation of this division shall be punishable by a fine of not more than $5.00.
(Code 1968, § 46-297; Ord. No. 72-1598, § 1(9), 9-6-72; Ord. No. 72-2309, § 1, 12-20-72)
Charter references: Penalty for ordinance violation, Art. II, § 12.
Cross references: Assessment of fines against corporations, § 16-76; payment of fines, § 16-78; credit against fines for incarceration, § 35-6 et seq.