(b) On or before the first day of October in each year, the district superintendent shall transmit to the commissioner of education and to the commissioner, in the form prescribed by it, a statement for the current fiscal year showing the taxable assessed valuation of real property of each city and town within the school district, the assessed valuation of such real property upon which the school tax has actually been levied, the state equalization rate or special equalization rate used to determine the apportionment of taxes, the full valuation of real property of each part of a city or town included in such school district, whether any school tax was apportioned pursuant to subdivision one-a of this section, and a list of the partial exemptions which the school authorities have by resolution adopted pursuant to this section, elected to include in the taxable assessed valuation of real property.

(c) The state equalization rate to be furnished by the commissioner shall be the rate established by the commissioner for the assessment roll on which school taxes are to be levied. When no state equalization rate has been established for such roll, the rate to be furnished shall be the rate established for the assessment roll immediately preceding the roll on which taxes are to be levied provided, however, that where a special equalization rate has been determined as provided in subdivision two of this section, that special equalization rate shall be furnished to the district superintendent for the purpose of equalization pursuant to this section. Where the commissioner determines that a city or town has implemented a reassessment at full value on the current roll, it may establish a special equalization rate of one hundred for that city or town and establish special equalization rates for the other cities or towns within that school district by adjusting the latest state equalization rates for those cities or towns to the appropriate current roll. In all cases in any given school district the state equalization rates or special equalization rates to be furnished by the commissioner for the apportionment of taxes shall have the same full value standard. Where the commissioner furnishes the same state equalization or special equalization rate for two or more of the cities and towns in a school district for use by that school district in the apportionment of taxes, the commissioner shall concurrently therewith notify the school district that school taxes may be apportioned in the manner provided by subdivision one-a of this section.

(d) (i) Such district superintendent shall also determine what proportion of any tax to be levied in such school district for school purposes during the current school year shall be levied upon each part of a city or town included in such school district by dividing the sum of the full valuation of real property in such part of a city or town by the total of all such full valuations of real property in such school district. Provided, however, that prior to the levy of taxes, the governing body of the school district may adopt a resolution directing such proportions to be based upon the average full valuation of real property in each such city or town over either a three-year period, consisting of the current school year and the two prior school years, or over a five-year period, consisting of the current school year and the four prior school years. Once such a resolution has been adopted, the proportions for ensuing school years shall continue to be based upon the average full valuation of real property in each such city or town over the selected period, unless the resolution provides otherwise or is repealed.

(ii) Such proportions shall be expressed in the nearest exact ten thousandths and the school authorities of such school district shall levy such a proportion of any tax to be raised in the school district during the current school year upon each part of a city or town included in such school district as shall have been determined by the district superintendent. A new proportion shall be determined for each school year thereafter by the district superintendent in accordance with the provisions of this section by the use of the latest state equalization rates. In any such school district that is not within the jurisdiction of a district superintendent of schools, the duties which would otherwise be performed by the district superintendent under the provisions of this section, shall be performed by the school authorities of such district. 1-a. When the commissioner has furnished the same state equalization or special equalization rate for two or more of the cities and towns in a school district for use by that school district in the apportionment of taxes, the school district may apportion its levy as follows:

(a) The district superintendent shall determine the amount of school tax to be raised from each city and town in the district in accordance with the provisions set forth in subdivision one of this section.

(b) For those cities and towns with respect to which the commissioner has furnished the same state equalization or special equalization rate, the amount of school tax to be raised in aggregate from each part of such city or town is the sum of the amounts determined for each such city and town in accordance with paragraph (a) of this subdivision. This aggregate amount of school tax shall be apportioned to each such city or town in proportion to the sum of the assessed value actually subject to taxation for school purposes plus the amount of assessed value partially exempt from taxation for school purposes pursuant to section four hundred twenty-five of this chapter. 2. If it is made to appear to the commissioner by a statement of the assessors of the city or town, subscribed and affirmed by them as true under the penalties of perjury, that there has been a change in the level of assessment since the last state equalization rate for the city or town was established, or, if it is made to appear to the commissioner that the state equalization rate established by it for a city or town is inequitable as applied to real property within the school district in such city or town, it shall determine a special equalization rate for such city or town or for such real property, as the case may be, which shall be used for the sole purpose of equalization under this section. Such special equalization rate as finally determined shall be furnished by such commissioner to the district superintendent of schools or the school authorities, as the case may be. 3. (a) Upon his own motion or, prior to the statutory date for the levy of school district taxes on the next subsequent assessment roll, at the request of a person liable to pay taxes upon real property in the school district, a district superintendent who failed to use one or more state equalization rates furnished pursuant to this section, or who made a mathematical error in determining full value or in apportioning the tax on the basis of full value, shall redetermine the full valuation of the real property of each part of a city or town within the school district and the proportion of the tax which should have been levied in each city or town or part thereof based upon the corrected full valuation. If such redetermination cannot be made prior to the extension of taxes for that year, the district superintendent shall cause the school district tax levy for the following year to be adjusted to account for the improper apportionment which resulted from his error, upon notice to the commissioner and the commissioner of education; provided, however, that the school authorities by resolution may elect to adjust the tax levy in the current year notwithstanding a redetermination of full valuation after the extension of taxes for the current year.

(b) Within thirty days of the receipt of a request for such redetermination, the district superintendent shall report his findings and determination to the person who made such request. Such person may appeal an adverse determination of the district superintendent, upon application to the commissioner within sixty days of the mailing of the report of the district superintendent.

(c) Not later than thirty days after receipt of a request for review of a determination by the district superintendent, the commissioner, upon notice to the commissioner of education, shall determine whether the district superintendent erred in his determination of full value or tax apportionment based thereon, for one or more of the reasons described in paragraph (a) of this subdivision. If the commissioner finds that such an error occurred, it shall issue an order, upon notice to the commissioner of education, directing the district superintendent to adjust the apportionment of the school district tax levy for the ensuing fiscal year to account for the improper apportionment which occurred as a result of the error of the superintendent.

(d) References herein to the district superintendent of schools shall be deemed to mean the school authorities of a school district which is not within the jurisdiction of a district superintendent of schools. 4. The provisions of this section shall apply to supplemental assessment rolls completed, verified and filed pursuant to section thirteen hundred thirty-five of this chapter, and the term "state equalization rate" as used in this section shall include the state equalization rate established for such supplemental assessment rolls pursuant to title one of article twelve of this chapter.