I'm adding a note to a long-ago post about finding a lost cat or dog:
If your flier is consistently torn down from one place every day, stake it out; sit in your car in a position that's inconspicuous but from which you can see the flier. When the de-flier comes along, write down their license plate number and take it to Animal Care and Control; they can find out the owner's address, so you can tell the police where to pick up the animal, confirming s/he lives with you by microchip scan.