Except as otherwise provided in Section 21-33-10, the governing authorities of any municipality shall have the power to change assessments, after the assessment roll, or rolls, of real and personal property have been finally approved, but not after the expiration of the fiscal year in which the taxes on said assessments are due and payable. The assessments may be reduced or increased for the same reasons and in like manner, as provided by law for the reduction and/or increasing of county assessments. Such change shall not be submitted to the state tax commission for approval.

Where a reduction is sought, the governing authorities shall require the owner of the property, or his duly authorized agent or attorney, to make a suitable application or petition, and where an increase is sought the application or petition shall be made by the assessor. The governing authorities shall have the right and power to consider the application or petition and to do any and all things necessary to determine whether or not it shall be allowed, and shall adopt an order rejecting or approving the application or petition. Said authorities may adopt an order to change the assessment so as to increase or decrease the assessment to the fair value of the property, or to cause the taxes to be charged to the person or property liable therefor.

The clerk shall carefully file and preserve, as a public record, in his office, all petitions or applications, and exhibits thereto, for either an increase or decrease in assessments as herein provided, for a period of three (3) years after the expiration of the fiscal year in which such petitions or applications were filed.