I haven't seen any reference to this in the laws I have seen.
The only reference that the CHL handbook makes is on p.51: Local Government Code LGC 229.001 Firearms; Explosives:
CHAPTER 229. MISCELLANEOUS REGULATORY AUTHORITY OF MUNICIPALITIES
Sec.A229.001. FIREARMS; EXPLOSIVES.A (a) municipality may not adopt regulations relating to the transfer, private
ownership, keeping, transportation, licensing, or registration of firearms, ammunition, or firearm supplies.
(b) Subsection (a) does not affect the authority a municipality has under another law to:
(1) require residents or public employees to be armed for personal or national defense, law enforcement, or another lawful purpose;
(2) regulate the discharge of firearms within the limits of the municipality;
(3) regulate the use of property, the location of a business, or uses at a business under the municipality ’s fire code,
zoning ordinance, or land-use regulations as long as the code, ordinance, or regulations are not used to circumvent the intent of Subsection (a) or Subdivision (5) of this subsection;
(4) regulate the use of firearms in the case of an insurrection, riot, or natural disaster if the municipality finds
the regulations necessary to protect public health and safety;
(5) regulate the storage or transportation of
explosives to protect public health and safety, except that 25
pounds or less of black powder for each private residence and 50
pounds or less of black powder for each retail dealer are not
subject to regulation; or
(6) regulate the carrying of a firearm by a person
other than a person licensed to carry a concealed handgun under Subchapter H, Chapter 411, Government Code, at a:
(A) public park;
(B) public meeting of a municipality, county, or other governmental body;
(C) political rally, parade, or official political meeting; or
(D) nonfirearms-related school, college, or professional athletic event.
(c) The exception provided by Subsection (b)(6) does not
apply if the firearm is in or is carried to or from an area
designated for use in a lawful hunting, fishing, or other sporting
event and the firearm is of the type commonly used in the activity.
(d) The exception provided by Subsection (b)(4) does not authorize the seizure or confiscation of any firearm or ammunition from an individual who is lawfully carrying or possessing the firearm or ammunition.