As a note--St. Michael's feast day is September 29th; St. Andrew's is November 30th.
In addition to police, St. Michael is the patron saint of:
against danger at sea against temptations ambulance drivers artists bakers bankers banking barrel makers battle boatmen coopers dying people emergency medical technicians EMTs fencing Greek Air Force greengrocers grocers haberdashers hatmakers (hatters and milliners) holy death knights mariners paramedics paratroopers radiologists radiotherapists sailors security guards sick people soldiers storms at sea swordsmiths watermen — England Germany — Coimbatore, India, diocese of Iligan, Philippines, diocese of Mobile, Alabama, archdiocese of Pensacola-Tallahassee, Florida, diocese of Rouyn-Noranda, Québec, diocese of San Angelo, Texas, diocese of Seattle, Washington, archdiocese of Sherbrooke, Canada, archdiocese of Springfield, Massachusetts, diocese of Toronto, Ontario, archdiocese of — Albenga, Italy Argao, Cebu, Philippines Basey, Samar, Philippines Brecht, Belgium Brendola, Italy Brussels, Belgium Cabo Rojo, Puerto Rico Caltanissett, Sicily, Italy Carpineto Sinello, Italy Castel Madama, Italy Cerveteri, Italy Cornwall, England Cuneo, Italy Dormagen, Germany Dunakeszi, Hungary Gaby, Italy Gravina, Italy Greccio, Italy Iklin, Malta London, England Marcianise, Italy Naranjito, Puerto Rico Papua, New Guinea Puebla, Mexico Salgareda, Italy San Miguel, Iloilo, Philippines San Miguel de Allende, Mexico Sant’Angelo Romano, Italy Saracinesco, Italy Sibenik, Croatia Siegburg Abbey Toronto, Ontario, city of Umbria, Italy Vallinfreda, Italy Zeitz, Germany
And Andrew is the patron saint of:
against gout against sore throats anglers fish dealers fish mongers fishermen maidens old maids single lay women singers Spanish armed forces spinsters University of Patras unmarried women women who wish to become mothers — Achaia Greece Russia Scotland — Constantinople, diocese of Grand Rapids, Michigan, diocese of Victoria, British Columbia, diocese of — Amalfi, Italy Antey-Saint-Andre, Italy Berchtesgaden, Germany Burgundy, France Cartosio, Italy Conflenti, Italy Encinasola, Huelva, Spain Grognardo, Italy Lampertheim, Germany Luqa, Malta Patras, Greece Plymouth, England Samolaco, Italy
That cop also has a shamrock anywhere he can get away with it. A common placement is on the bottom of his service pistol's magazine. It'll either be a glued-on patch, a sticker, or something like that. Ditto the fire department: firefighters will get reflective shamrock stickers and put them on their helmets, their air tanks, and occasionally on the BRT (Big Red Truck) itself.