Truck Parking Safety Improvement Act This bill directs the Department of Transportation (DOT) to provide competitive grants for projects that provide public parking for commercial motor vehicles and improve the safety of commercial motor vehicle drivers. States, metropolitan planning organizations, tribal governments, and local governments are eligible for these grants. The grants must be used for projects on federal-aid highways or a facility with reasonable access to such a highway or a freight facility. In providing grants, DOT must determine that there is a shortage of commercial motor vehicle parking capacity in the corridor in which the project is located; the eligible entity has consulted with motor carriers, commercial motor vehicle drivers, public safety officials, and private providers of commercial motor vehicle parking regarding the project; the project will likely increase the availability or utilization of commercial motor vehicle parking, facilitate the efficient movement of freight or improve highway safety, traffic congestion, and air quality; and the eligible entity has demonstrated the ability to provide for the maintenance and operation of the facility. To the maximum extent practicable, DOT must select grant projects that maximize the geographic dispersion of new commercial motor vehicle parking capacity across the United States.