N.H. Rev. Stat. Ann. § 246:39

No overhead bridge or other structure shall hereafter be constructed across a railroad track in this state with less than 22 feet between the top of the rails and the lowest point of the overhead structure, except with the written consent of the department of transportation, and no railroad corporation shall receive or haul any freight car exceeding 16 feet in height from the rails to the top of the running board.