According to the pilot, prior to the flight, he determined the highest obstacle enroute was 6,100 ft with several 5,000 to 5,500 ft peaks along the route. In addition, he noted that during the flight, the end of evening nautical twilight would occur. After departure, he dialed 5,500 ft into the autopilot and leveled off. He went to don the night vision goggles and noted that they were on the copilot seat on top of an aircraft logbook. He went to move the logbook to the pilot door compartment, where it was typically stowed for flight, and decided to check the flight times against the times that maintenance was due. At that point, he noticed the cloud ceiling was lowering and dialed in 5,000 ft into the autopilot, then “went back heads down” to continue his review of the logbook. Then, the flight nurse asked for an updated estimated time enroute, and when the pilot looked up, he saw the helicopter was approaching a tree covered peak. He applied aft cyclic in order to climb; however the tail boom struck several trees, resulting in the vertical stabilizer separating from the tail boom. The pilot subsequently performed a forced landing to a road, which resulted in substantial damage to the fuselage and tail boom. The pilot reported no preimpact mechanical malfunctions or failures with the helicopter that would have precluded normal operation.