The private pilot reported that he was conducting his initial takeoff when the window on the cockpit door came open. He reached with his left hand to close the window and simultaneously tried to abort the takeoff. When he looked up, he observed the airplane departing the left side of the runway. He was unable to stop the airplane before it collided with perimeter trees. According to an inspector with the Federal Aviation Administration, the airframe was damaged, including a buckled engine firewall. The pilot reported no mechanical malfunctions or failures that would have precluded normal operation of the airplane.