§292.1. Transportation and storage of firearms in privately owned motor vehicles
A. Except as provided in Subsection D of this Section, a person who lawfully possesses a firearm may transport or store such firearm in a locked, privately-owned motor vehicle in any parking lot, parking garage, or other designated parking area.
B. No property owner, tenant, public or private employer, or business entity or their agent or employee shall be liable in any civil action for damages resulting from or arising out of an occurrence involving a firearm transported or stored pursuant to this Section, other than for a violation of Subsection C of this Section.
C. No property owner, tenant, public or private employer, or business entity shall prohibit any person from transporting or storing a firearm pursuant to Subsection A of this Section. However, nothing in this Section shall prohibit an employer or business entity from adopting policies specifying that firearms stored in locked, privately-owned motor vehicles on property controlled by an employer or business entity be hidden from plain view or within a locked case or container within the vehicle.
D. This Section shall not apply to:
(1) Any property where the possession of firearms is prohibited under state or federal law.
(2) Any vehicle owned or leased by a public or private employer or business entity and used by an employee in the course of his employment, except for those employees who are required to transport or store a firearm in the official discharge of their duties.
(3) Any vehicle on property controlled by a public or private employer or business entity if access is restricted or limited through the use of a fence, gate, security station, signage, or other means of restricting or limiting general public access onto the parking area, and if one of the following conditions applies:
(a) The employer or business entity provides facilities for the temporary storage of unloaded firearms.
(b) The employer or business entity provides an alternative parking area reasonably close to the main parking area in which employees and other persons may transport or store firearms in locked, privately-owned motor vehicles.
Acts 2008, No. 684, §1.
Looks like the answer to your question is YES.