In the Presidential metro, after you exit the hall with a few flags and the statues of presidents immediately turn right, it is on the bench there.
By a skeleton on a bench near some of the tracks. To find this is easy. After you exit M.A.R.Go.T.'s control room you will see 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, you will see a skeleton with a .32 pistol and a police hat.
One is also located on the floor in the office with the safe and two cash registers in the Old Olney S. Wilson Building.
A second one is located 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.
A police hat can also be found on top of a television in the Grower's shack.
Inside the Point Lookout Lighthouse. On the steps about halfway up, near a skeleton. It may clip into stairs, making it unobtainable.
One can also be found in the cryo lab among a wide variety of junk.
Notes
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.
In the Presidential metro, after you exit the hall with a few flags and the statues of presidents immediately turn right, it is on the bench there.
