A police dog is a dog trained specifically to help the police. The term used by the police is "K-9," a homophone of canine, which is Latin for "dog." The police officer who handles the police dog is called a "K-9 unit." The dogs almost always live with the police officer who handles them and his or her family. Dogs will almost always be loyal to only one master, it is therefore impossible for police officers to share a dog unless the officers live with each other.
Police dogs do many jobs. The most common type of police dog job is public enforcement. These dogs are used to chase a fleeing suspect and hold them until human officers can arrest the suspect. They can also be used in something called "hold and bark" where the police officer will hold the dog back while he or she barks loudly at the suspect, basically saying "don't run away" (or maybe they are saying "please run away so I can chase you and bite you"). They can also be used to search buildings where a dangerous suspect may be hiding. Very often simply by threatening to let the dog in, the police can get a suspect to surrender. Most police agencies now train their dogs not to bite if the suspect puts up their hands and stops running. Common breeds for this role tend to be large, intimidating dogs like German Shepherds, Rottweilers, or Doberman Pinschers ("Pinsch" is German for "bite")
Less common, but no less important are search and rescue dogs. These dogs are not used to catch bad guys, rather they are sent in to help find people who are lost or hurt. They use smell to track where a person has gone and then to find them. If a building falls down these dogs can also be used to find people trapped in the rubble. These dogs are also prized by ski patrol (kind of police/paramedics at ski areas). They are very good at finding people buried by avalanche. Bloodhounds are commonly used for there keen nose but also Australian Shepherds, Golden Retrievers and labs are used as well.
Detection dogs are used to find drugs or bombs hidden by smugglers or terrorists. The US Constitution states that a citizen has the right to refuse to let the police search their property without permission unless the police have a good reason to suspect illegal activity. Usually the police will ask a suspect if they can search the suspect's car. If the suspect says "no" the police can allow a drug dog to sniff around the outside of the car. If the dog smells drugs then the police have "probable cause" to search further.
Sometimes the police need to find someone who has died. In this case they will use a cadaver dog (a dead human body is called a cadaver). These dogs are trained to track the smell of a dead body. Depending on the weather a dead body can have a very strong smell for some time, however if decomposition hasn't had time to really get going yet, or if it is already nearly complete the smell is not strong enough to be detected by humans. However dogs can smell several hundred times better than people.