Munich police chief Hubertus Andrae told reporters the suspect, identified only as a Bavarian-born German citizen, flew to Munich airport from Athens on Monday and spent the night in the airport.
Witnesses told police as the man rode the subway toward the city Tuesday he was talking to himself in English, then suddenly began punching another, apparently randomly chosen, passenger in the face, pummeling him until he was bloody.
Police were called and when the suspect got off at the suburban Unterfoehring station, two officers began questioning him. Surveillance video shows one officer holding a pad of paper and pen taking notes when the suspect suddenly shoved him with "extreme violence" toward an oncoming train, Andrae said.
In the ensuing struggle the suspect grabbed the officer's pistol from its holster, and opened fire at both of the officers. He missed the officer whose weapon he took, but hit his colleague in her head as he emptied the eight-shot magazine. Two bystanders were also injured, and are believed to have been hit by shots fired by the suspect.
The officer hit in the head appears to have fired at least one shot, hitting the suspect in the buttocks. Despite the wound, he was able to flee and was apprehended outside by other officers arriving on the scene.
The injured officer was rushed to a nearby hospital and was still in life-threatening condition on Wednesday, Andrae said. The bystanders were also treated and are stable.
Andrae said police had been in contact with the suspect's father with whom he had been living in the U.S., and said the suspect apparently had a criminal record there.
He did not give further details but a police source confirmed German media reports that the suspect's name is Alexander B. and that he had been living in Colorado. Bild newspaper reported he was staying in Fort Collins, but the source could not confirm that.
In addition to some 200 witnesses to interview, Andrae said police also have video surveillance footage from multiple locations to review and are still working on a complete picture of how the attack unfolded. The suspect has so far refused to talk with police.