LABOR CODE
TITLE 2. PROTECTION OF LABORERS
SUBTITLE B. RESTRICTIONS ON LABOR
CHAPTER 52. MISCELLANEOUS RESTRICTIONS
SUBCHAPTER G. RESTRICTIONS ON PROHIBITING EMPLOYEE TRANSPORTATION OR STORAGE OF CERTAIN FIREARMS OR AMMUNITION
Sec. 52.061. RESTRICTION ON PROHIBITING EMPLOYEE ACCESS TO OR STORAGE OF FIREARM OR AMMUNITION. A public or private employer may not prohibit an employee who holds a license to carry a concealed handgun under Subchapter H, Chapter 411, Government Code, who otherwise lawfully possesses a firearm, or who lawfully possesses ammunition from transporting or storing a firearm or ammunition the employee is authorized by law to possess in a locked, privately owned motor vehicle in a parking lot, parking garage, or other parking area the employer provides for employees.
Added by Acts 2011, 82nd Leg., R.S., Ch. 1058, Sec. 1, eff. September 1, 2011.
Sec. 52.062. EXCEPTIONS. (a) Section 52.061 does not:
(1) authorize a person who holds a license to carry a concealed handgun under Subchapter H, Chapter 411, Government Code, who otherwise lawfully possesses a firearm, or who lawfully possesses ammunition to possess a firearm or ammunition on any property where the possession of a firearm or ammunition is prohibited by state or federal law; or
(2) apply to:
(A) a vehicle owned or leased by a public or private employer and used by an employee in the course and scope of the employee's employment, unless the employee is required to transport or store a firearm in the official discharge of the employee's duties;
(B) a school district;
(C) an open-enrollment charter school, as defined by Section 5.001, Education Code;
(D) a private school, as defined by Section 22.081, Education Code;
(E) property owned or controlled by a person, other than the employer, that is subject to a valid, unexpired oil, gas, or other mineral lease that contains a provision prohibiting the possession of firearms on the property; or
(F) property owned or leased by a chemical manufacturer or oil and gas refiner with an air authorization under Chapter 382, Health and Safety Code, and on which the primary business conducted is the manufacture, use, storage, or transportation of hazardous, combustible, or explosive materials, except in regard to an employee who holds a license to carry a concealed handgun under Subchapter H, Chapter 411, Government Code, and who stores a firearm or ammunition the employee is authorized by law to possess in a locked, privately owned motor vehicle in a parking lot, parking garage, or other parking area the employer provides for employees that is outside of a secured and restricted area:
(i) that contains the physical plant;
(ii) that is not open to the public; and
(iii) the ingress into which is constantly monitored by security personnel.
(b) Section 52.061 does not prohibit an employer from prohibiting an employee who holds a license to carry a concealed handgun under Subchapter H, Chapter 411, Government Code, or who otherwise lawfully possesses a firearm, from possessing a firearm the employee is otherwise authorized by law to possess on the premises of the employer's business. In this subsection, "premises" has the meaning assigned by Section 46.035(f)(3), Penal Code.
Added by Acts 2011, 82nd Leg., R.S., Ch. 1058, Sec. 1, eff. September 1, 2011.
Sec. 52.063. IMMUNITY FROM CIVIL LIABILITY. (a) Except in cases of gross negligence, a public or private employer, or the employer's principal, officer, director, employee, or agent, is not liable in a civil action for personal injury, death, property damage, or any other damages resulting from or arising out of an occurrence involving a firearm or ammunition that the employer is required to allow on the employer's property under this subchapter.
(b) The presence of a firearm or ammunition on an employer's property under the authority of this subchapter does not by itself constitute a failure by the employer to provide a safe workplace.
(c) For purposes of this section, a public or private employer, or the employer's principal, officer, director, employee, or agent, does not have a duty:
(1) to patrol, inspect, or secure:
(A) any parking lot, parking garage, or other parking area the employer provides for employees; or
(B) any privately owned motor vehicle located in a parking lot, parking garage, or other parking area described by Paragraph (A); or
(2) to investigate, confirm, or determine an employee's compliance with laws related to the ownership or possession of a firearm or ammunition or the transportation and storage of a firearm or ammunition.
Added by Acts 2011, 82nd Leg., R.S., Ch. 1058, Sec. 1, eff. September 1, 2011.
Sec. 52.064. CONSTRUCTION OF PROVISION RELATING TO IMMUNITY FROM CIVIL LIABILITY. Section 52.063 does not limit or alter the personal liability of:
(1) an individual who causes harm or injury by using a firearm or ammunition;
(2) an individual who aids, assists, or encourages another individual to cause harm or injury by using a firearm or ammunition; or
(3) an employee who transports or stores a firearm or ammunition on the property of the employee's employer but who fails to comply with the requirements of Section 52.061.
Added by Acts 2011, 82nd Leg., R.S., Ch. 1058, Sec. 1, eff. September 1, 2011.
You beat me to it. Thanks for posting the statute. 
... I'm retired