Burr shot Hamilton in the hip bone and it ricocheted and hit several major organs. His doctor, who stood nearby with others who had their backs turned to the duel later said when he rushed to Hamilton all he said was "doctor this is surely a fatal shot" or something like that and passed out.
Later, they managed to awaken him in the boat headed for shore, and he saw his pistol sitting outside the dueling pistol box...he said " be careful , doc...that pistol is cocked but has not yet discharged. As I said before the match, I had no intention of firing a shot."
Burr claimed that Hamilton fired and missed, then burr shot him. It looks to many like Burr simply shot Hamilton, and as he fell to the ground he shot a round up into the bottom of a tree limb some 13 or 14 feet above Burr, and 5 paces to his right (Burrs left). Apparently. Hamilton didnt even remember his gun firing...or in his dying state he was super worried about a coverup...which seems highly unlikely. Burr had told everyone heading up to the match that he intended to kill Hamilton..and when he was told that Hamilton had died from a shot to the hip, he said "I wish I would have hit him in the head."
Edit...Hamiltons son Phillip had been killed in a duel right next to where this duel took place, on the previous year. Bad JuJu .