Answer:
Horses that are selected and trained for the police are probably bred specifically in their facilities for the right temperment, and bloodlines to create a very well rounded horse. Then they will have to go through training to bomb proof (bomb proofing is training to keep horses calm in all situations so that they dont spook) and desensitize them. The final product would be your police horse, extremely well trained to be in tune with it's rider and to ignore distractions around itself.