On July 30, 2014, about 1030 central daylight time, a Bell 206B, N866H, sustained substantial damage during engine start-up at the David Wayne Hooks Airport (DWH), Spring, Texas. The pilot was not injured. The helicopter was owned by Helicopter Services Inc. and operated by the Harris County Sheriff's Office as a local public aircraft flight. Visual meteorological conditions prevailed at the time of the accident. No flight plan was filed. The helicopter was departing on a local flight. The pilot reported that he completed the preflight of the helicopter while it was still in the hangar, after which time the helicopter was moved onto the ramp. When the pilot arrived to start the helicopter, he was distracted by a phone call on his cellular phone and did not do an exterior check of the helicopter. The main rotor tie-down was still attached when the pilot engaged the engine. He was monitoring the cockpit gauges during the engine start when he noticed another officer approaching the helicopter waving his hands. He heard a "thump" and he initiated an emergency shutdown. The pilot stated that the engine start was aborted at 15 percent N1 (compressor speed), 25 percent N2 (power turbine speed), rotor rpm was less than 20 percent NR (main rotor rpm), and the TOT (turbine outlet temperature) did not exceed startup limits. He reported that there was no malfunction or system failure of the helicopter before the accident. The examination of the helicopter revealed that the tie-down strap had broken during the engine start and became caught on the tail rotor output shaft. The strap hit the tail boom and dented and gouged about the last two feet of the tail boom which required the skin to be replaced. The main rotor blade tip cap pulled loose. The main rotor blades were still serviceable, but they were replaced because they were 120 hours from the required replacement interval. The tail rotor blades were dented beyond limits and were replaced. The vertical fin was gouged; and although the honeycomb panel was repairable, the vertical fin was replaced instead of waiting for it to be overhauled. The tail rotor gearbox, the tail rotor hub, and the freewheeling unit needed to be inspected for sudden stoppage, which resulted in the units being overhauled. It was determined that the aggregate damage would affect the structural strength or performance of the helicopter and required major repair or replacement; therefore it was considered substantial damage.