If any city in this state which has established a civil service system in compliance with the requirements of this chapter shall change its form of municipal government, such civil service provisions as previously have been established shall continue under the new form of municipal government except as to those provisions which the governing body of the city may see fit to change within the limitations described in this chapter. The governing body of the city, after the change in its form of government, shall designate, as described in section 40-44-08, the departments, classes of employees, and appointive officials of the city who shall come under the civil service, and it subsequently may add thereto except as restricted by the provisions of this chapter.