An arrest report 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, at least in the 23rd century, filed arrest reports when they did so. For instance, Captain James T. Kirk ordered Spock to fill out an arrest report on Harcourt Fenton Mudd after they brought him into custody.
The precise details that were required on an arrest report under Federation law were unknown in their entirety. However, they included a medical evaluation, as Spock ordered Nurse Chapel to append her assessment of Mudd's health to his larger arrest report. (TAS: "Mudd's Passion")