What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
The pilot entered the runway environment and closed the top hatch of the door to prepare for takeoff, the top half was left open during taxi to allow more airflow and a cooler cabin. After shutting the door there was no “door unsafe” annunciator on the annunciator panel. The aircraft took off on runway 12 and climbed straight out. At approximately 2,500 feet and 2 miles off of the departure end of the runway the rear passenger tapped the pilot on the shoulder indicating it looked like there was a crack in the back half of the door. The pilot looked down and placed his hand in the area of the door, at which point the top half of the door abruptly swung open and dislodged itself from the aircraft. The pilot's arm came out of the plane with it; however, he was quickly able to pull it back in without any injury. The pilot immediately declared an emergency and made a right turn to enter a left downwind for runway 12 where the aircraft landed several minutes later. There were no injuries to the pilot, or passengers, and after an inspection by the fire crew on taxiway privacy data omitted the pilot taxied back to Hamilton jetport.
As the FAA filed it
THE PILOT ENTERED THE RUNWAY ENVIRONMENT AND CLOSED THE TOP HATCH OF THE DOOR TO PREPARE FOR TAKEOFF, THE TOP HALF WAS LEFT OPEN DURING TAXI TO ALLOW MORE AIRFLOW AND A COOLER CABIN. AFTER SHUTTING THE DOOR THERE WAS NO “DOOR UNSAFE” ANNUNCIATOR ON THE ANNUNCIATOR PANEL. THE AIRCRAFT TOOK OFF ON RUNWAY 12 AND CLIMBED STRAIGHT OUT. AT APPROXIMATELY 2,500 FEET AND 2 MILES OFF OF THE DEPARTURE END OF THE RUNWAY THE REAR PASSENGER TAPPED THE PILOT ON THE SHOULDER INDICATING IT LOOKED LIKE THERE WAS A CRACK IN THE BACK HALF OF THE DOOR. THE PILOT LOOKED DOWN AND PLACED HIS HAND IN THE AREA OF THE DOOR, AT WHICH POINT THE TOP HALF OF THE DOOR ABRUPTLY SWUNG OPEN AND DISLODGED ITSELF FROM THE AIRCRAFT. THE PILOT'S ARM CAME OUT OF THE PLANE WITH IT; HOWEVER, HE WAS QUICKLY ABLE TO PULL IT BACK IN WITHOUT ANY INJURY. THE PILOT IMMEDIATELY DECLARED AN EMERGENCY AND MADE A RIGHT TURN TO ENTER A LEFT DOWNWIND FOR RUNWAY 12 WHERE THE AIRCRAFT LANDED SEVERAL MINUTES LATER. THERE WERE NO INJURIES TO THE PILOT, OR PASSENGERS, AND AFTER AN INSPECTION BY THE FIRE CREW ON TAXIWAY ^PRIVACY DATA OMITTED^ THE PILOT TAXIED BACK TO HAMILTON JETPORT.