(a) The oath of office of the county treasurer must be entered on the minutes of the county governing authority and filed in his office. His official bond must be filed and recorded in such office.

(b) When one or more sureties on the bond of the county treasurer own real estate in any county or counties other than the county in which the treasurer holds office, such bond, within 30 days after the execution thereof, shall be recorded in the county or counties wherein the real estate is situated, by the county governing authority, or such bond shall be recorded within 30 days after its execution by the authority in the book of record of bonds of county officers. After the treasurer's bond is accepted and recorded in the county in which the treasurer holds office, the county governing authority of such county shall forward the same to the county governing authority in each county in which any one or more sureties on the bond own any real estate; such county governing authority to whom the bond is sent shall record the same in accordance with this subsection.