"Police Operation" was published by Astounding Science Fiction in July of 1948. The parallel worlds or versions of Earth are divided into five levels. In this conceptual universe, humans colonized Earth from Mars. The timeline we occupy wasn't colonized very successfully, and the people haven't any recollection of the colonization, so we are in the fourth level. But the transplanting in the first level was outstanding, thus, the Paratime Police originated there.
The illustrations are by Edd Cartier. This story's copyright wasn't renewed. The video sound effect "Crazy Brass" is a creation of musiforvideo.com.
Police Operation from Paratime Series; Illustrations
The Essential Works of H. Beam Piper