Any county or city is authorized to establish a department of finance.  The county boards of supervisors and the city councils shall have the option of appointing the director of the department of finance or delegating that authority to the county administrator or city manager.   If a county or city exercises this option to establish a department of finance, the director of the department shall assume the duties and responsibilities of commissioners of the revenue and treasurers as set out in Chapter 31 of Title 58.1, Code of Virginia, that relate to local financial matters.