PA-60 Aerostar Captain reported being notified by a passenger of the aircraft cabin door not latched during the climb; then the door unlatched and separated from the aircraft. The Captain returned to the departure airport and landed safely; the passengers were not injured but the Captain suffered an arm injury due to the force of the relative wind.

Narrative

Prior to takeoff on runway XX in ZZZZ I had verified that the door latch indicators were indeed showing latched; and that we had no cabin door unsafe annunciator per normal procedure. On climbout my rear passenger tapped my shoulder to make me aware that our cabin door was not fully closed; at that time I looked down and saw that the latching indicators were showing latched; but we had a small gap between the fuselage and the aft side of the door. In addition to this my copilot said that he did not see a cabin door unsafe annunciator. At this time I had taken my left hand and placed it on the door handle making sure to not push or twist it as that would possibly cause the door to completely unlatch. As soon as I placed my hand down by the door; the door raised up and completely separated from the fuselage; along with the door; 3/4 of my arm were carried outside with the oncoming wind. Due to this my arm was deeply bruised accompanied by a moderate pain. After I had diagnosed the situation I verified the passengers were un-injured and chose to [request assistance] and return to ZZZZ for a safe landing.