I agree with the previous answers and you would also most likely be charged for the service and your past due account sent to collections when you refused to pay.
A much better solution would be to voice your concerns about charges and the quality of service when making the next appointment. I would expect a vet or assistant to explain to you that when you were there last time the appointment covered a certain amount of time and the charges reflect the time. If your dog still has issues then more time may be necessary to treat the dog and you can expect more charges. In the alternative you could just go to another vet.
Please be sure to indicate the best answer. If this answer was helpful, please mark as helpful below. Only. If and until you and I sign an Agreement for Legal Services, I am not your attorney. These answers are provided for informational and/or novelty purposes
Walking out of a restaurant after eating without paying likely would result in the person being arrested.
Walking out of a veterinarian's office without paying and without causing a disturbance likely would result in a police officer telling the office personnel to sue the person in court. It is doubtful that a police officer would arrest the person or forward the information to a prosecutor for a criminal charge to be filed against the person.
If you know beforehand that you are not going to pay the vet, why are you wasting everyone's time taking the dog back to the vet? If the vet really want to examine the dog (perhaps to learning something new), you should come to an agreement with the vet that there would be no charges for this particular visit before you come.
I would agree with the opinion that the best way to deal with this (and avoid disputes, lawsuits or police) is direct problem-solving with the business. Tell them what happened and what you expect on the next visit. If they can't swing you a free visit to make up for the mix-up or at least make you happy in some way that they are being fair... then vote with you feet and go to another vet.