One is located on the floor in the office with the safe and two cash registers.
One in the center of the Old Olney S. Wilson Building. It is accessed by jumping from a ledge adjacent to the fallen GNR billboard onto the empty deathclaw cage. The police hat is next to a skeleton on a small platform at eye level.
After exiting the hall with a few flags and the art deco sculptures, immediately turn right, where one can be found on a bench.
By a skeleton on a bench near some of the tracks. After exiting M.A.R.Go.T.'s control room, there will be an American flag. Go that way and turn left towards the tracks. While facing the tracks, make another left. Go towards the caved-in part of the tracks, and near the wall, there will be a skeleton with a .32 pistol and a police hat.
A police hat can be found on top of a television in the Grower's shack.
It seems the police officers in Washington, D.C. before the Great War used .32 pistols, as police hats are commonly found with .32 pistols next to skeletons.