Forgot to add, the police chief nor mayor have the authority to terminate employment of officers. "Firing" by the chief is showmanship in an effort to appease or affect a certain response. Officers are hired by a Civil Service Commision so would also be fired by the same group. Which is why it is commonly reported that the chief's decision is overturned. The Commission is typically made up by volunteers who are then chosen and confirmed by the city council. Both sides bring forth their case and await a decision. This decision may be challenged by other means but it is generally the first steps.