Search and Rescue dogs are generally owned and trained by specialized dog trainers, not the cops. The scent-tracking skills for following people are differently trained from drug and explosives detecting dogs Basically a search dog needs to walk towards and follow what they smell, and a detecting dog needs to sit down when they catch a smell so they have different training methods.

Source; Hung out with Search and Rescue dog trainers and listened to them carefully not directly talk shit about the police dogs.