They don't own the name or designation. As long as you are not wearing any sort of an issued badge printed on the clothing, or a department name that would falsely identify you as a police officer you should be OK.
Check the statutes in your state. Our statutes in Illinois say nothing about K9 related clothing, wording, or statements as long as a department name is not included.
In cooler weather I often wear a leather Bayern Polizei Diensthundeführer jacket which is the German equivalent of a K9 handler.
Perfectly legal in my state as it is from a foreign department and bears no resemblance to anything worn in the states and has no badge. It is considered "for collector purposes only".
Around here, no one but me knows what it is anyway. They probably couldn't find Germany on a labeled map.
Bear, Anna, Molly, Ossie, and The Countess Lisl von Schlaf
An Unhappy German is a Sour Kraut!