An arrest report was a report that documented a legal arrest. It was the responsibility of the party making the arrest, or their designees, to submit one to the proper authority. Starfleet officers could arrest civilians and filed arrest reports when they did so.
In 2269, Captain James T. Kirk ordered Spock to fill out an arrest report on Harcourt Fenton Mudd after they brought him into custody. Later, Spock ordered Nurse Chapel to append her assessment of Mudd's health to his larger arrest report. (TAS: "Mudd's Passion")