I assume you literally mean "did Hitler personally kill a person," as in with his own hands.

In a narrow sense the answer is perhaps, but it's not likely. He served on the Western Front during the First World War, where he was close to combat, though generally behind the lines as a messenger. He was awarded the Iron Cross for bravery, but the citation does not mention any sort of aggressive act against enemy forces. Indeed, I do not know if he fired a weapon in combat during the war. In Mein Kampf he does not explicitly say that he killed enemy troops in anger, which is telling because the text is otherwise so filled with lies and half-truths, all of which were designed to advance his political position.

Years later, in 1934, Hitler played a personal role in the Night of the Long Knives. In Munich, he and an entourage of bodyguards and cronies supposedly found SA leader Edmund Heines in bed with a male lover during an early morning raid. The two were quickly killed on Hitler's orders. This fact was heavily emphasized in party propaganda to build support for the purge with the public, meaning that it's not necessarily reliable as a historical fact. So perhaps he was directly involved with political assassinations, but there's no account that indicates that he 'pulled the trigger.'

The accepted account of Hitler's death is that he and Eva Braun committed suicide together. They consumed cyanide, then Hitler shot himself. Perhaps one could argue that he was responsible for her death in some sense.

Finally. Your question leads to complications because so many people died on Hitler's orders (in combat or otherwise) that it's almost irrelevant as a historical fact whether or not he ever actually pulled the trigger. We know for certain that he ordered many millions of people to be killed.