Again... After Oswald was brought in from the theater, everyone gathered inside the office of Capt. Westbrook. This office is where the officers filled out their arrest reports.
Inside this office was Westbrook, Barrett and Oswald's wallet (with Oswald and Hidell identifications inside and taken from him by Bentley during the car ride from the theater to headquarters).
Think about it.
If you read what they all said and wrote, they showed up in the basement of the Municipal building, and brought Oswald up the back elevator to the DPD offices on the third floor. The party first went to the Homicide office, where they deposited Oswald and the wallet with Baker and other members of Fritz team. Hill and Baker conversed about possession of the revolver, the result being that Hill kept it. Then the arresting party proceeded to the squad room in the Personnel office. Bentley and Lyons went to the hospital to have their injuries examined, while the rest of the party set to writing reports. At some point after Bentley and Lyons left, Westbrook entered the squad room, saw the revolver lying on a desk, and sent for Lt Baker to come get it. At this point, Hill, Carroll, and McDonald put their initials on the weapon and turn it over.