The United States Air Force Air Police was a United States Air Force law enforcement agency responsible for defending airbases and facilities.
In 1969, Lieutenant Colonel Fellini, a staff sergeant and two airmen served in the Air Police at the US 498th Airbase Group. (TOS: "Tomorrow is Yesterday")
In reality, the Air Police had been renamed "United States Air Force Security Police" in 1966, three years prior to the supposed timeframe of the episode.
Kirk referred to it solely by the name "Air Police."