When any officer to whom this chapter relates shall succeed himself in office or has been elected to succeed himself in office or has been elected to succeed himself in a subsequent term, such officer or the surety on his bond either for the current term or for the term which has or shall have expired, or for a term about to begin, may file with the official or the county or municipal authority having jurisdiction to cite for accounting a petition asking that an accounting be had as to the acts of such officer during the term which has ended or is about to end. Such official or county or municipal authority shall then cause a citation to issue and be served on the officer and the sureties on his bonds for both terms, except such of them as shall be party to or join in the petition; and such further proceedings shall be had as are provided for in Code Section 45-8-20 in cases of citation for accounting. In the order or judgment rendered by the official or county or municipal authority conducting the accounting, or, in case of appeal, in the judgment of the court, the condition of the accounts of such officers shall be stated as between the two terms and as between the sureties for the respective terms; and the order or judgment shall set the terms upon compliance with which the sureties on the bond for the expired or expiring term shall be discharged or liability as to taxes, revenues, and public moneys satisfied; and it shall also settle and determine between the sureties in the respective bonds the matters for which each is or may be liable.