If the petition discloses that it involves the determination of any public right or interest of this state or of any county or municipality thereof, the process or notice, in order to affect the state, the county, or the municipality, shall be served:

(1) In the case of the state, upon the Attorney General;

(2) In the case of a county, upon the judge of the probate court or, if the judge of the probate court is disqualified, upon the clerk of the superior court; or

(3) In the case of a municipality, upon the mayor of the municipality or, if there is no mayor or if the mayor is disqualified, upon a majority of the members of the council or other governing body of the municipality.