Whether a dog is purchased for the handler by the department they are employed with or if the handler purchases the dog with their personal funds all depends upon the department they work for. I have seen both methods used. Some departments will purchase a "green" dog and then have an in-house trainer work with the dog and handler while others have contract with trainers who conduct the training. Some departments will purchase the dog as well as the training of the dog and handler from a vendor. Best bet to have your questions answered would be to make contact with a K-9 handler from your area and ask him/her. Costs vary as does the training. I have never met a K-9 handler that did not have at least a few years on the street under his/her belt before being assigned to the K-9 Unit.
Go ahead and run.....my k-9 partner loves the exercise