Truck Parking Safety Improvement Act This bill directs the Department of Transportation (DOT) to provide competitive grants to Indian tribes, states, metropolitan planning organizations, and local governments for projects that provide parking for commercial motor vehicles and improve the safety of commercial motor vehicle drivers on federal-aid highways or on a facility with reasonable access to such a highway or a freight facility. In providing grants, DOT must prioritize applicants that demonstrate a shortage of commercial motor vehicle parking capacity in the corridor in which the project is located; consultation with motor carriers, commercial motor vehicle drivers, public safety officials, and private providers of commercial motor vehicle parking; the project will likely increase the availability or utilization of commercial motor vehicle parking, facilitate the efficient movement of freight, and improve highway safety, traffic congestion, and air quality; and the ability to provide for the maintenance and operation of the facility.