(b) Beginning with the levy of taxes on the first assessment roll with a taxable status date occurring on or after December third, nineteen hundred eighty-one, the legislative body of any special assessing unit which is a city shall annually certify the base proportion, adjusted base proportion or adjusted proportion, whichever is appropriate, for each such class applicable to such special assessing unit, to the commissioner of finance of such city. Such certification shall also be filed with the commissioner at the same time.

(c) Beginning with the levy of taxes on the first assessment roll with a taxable status date later than December third, nineteen hundred eighty-one, the legislative body of each such special assessing unit and each municipal corporation, except a county wholly within a city, which includes a portion of such special assessing unit and which levies taxes on the assessment roll of such special assessing unit, shall annually allocate to each such class a share of such municipal corporation's tax equal to the base proportion, adjusted base proportion or adjusted proportion as certified in accordance with paragraph (a) or paragraph (b) hereof.

(d) For purposes of the allocation of taxes among classes in a town or county special district that is not a portion, or a zone of assessment located within a special assessing unit that is not a city, beginning with the levy of taxes on the first assessment roll with a taxable status date after December third, two thousand, the legislative body of each such special assessing unit shall annually allocate to each class located within such special district and effective for the levy of taxes on the first assessment roll with a taxable status date after December thirty-first, two thousand two, each zone of assessment, a share of such special district's or zone of assessment's tax equal to the base proportion or adjusted proportion as certified in accordance with paragraph (a) of this subdivision. 2. (a) Any city wholly situated in a special assessing unit which would otherwise be governed by the provisions of article nineteen of this chapter shall be governed by the provisions of this article if it adopts a local law providing that such city taxes shall be levied on the roll of the special assessing unit. Such local law shall be adopted not later than sixty days before the last date for the levy of its taxes. A copy of such local law shall be furnished to the assessor of such special assessing unit within thirty days after its adoption. In such event, such special assessing unit shall deliver that portion of its roll applicable to such city. Any local law adopted pursuant to this subdivision shall be effective for all subsequent tax years until repealed by such city.

(b) Any village wholly situated in a special assessing unit which would otherwise be governed by the provisions of article nineteen of this chapter shall be governed by the provisions of this article if it adopts a local law as provided in subdivision three of section fourteen hundred two of this chapter. 3. In a special assessing unit which is not a city, the governing body of any school district, and the legislative body of any village or city which has elected to be governed by the provisions of this article, may, by adopting a local law, or in the case of school districts, a resolution, allocate to class one property that share of such municipal corporation's tax levy equal to the base proportion, adjusted base proportion or adjusted proportion, whichever is appropriate, for such property and allocate the remainder of the tax levy to the remaining classes as a whole. 4. Nothing in section eighteen hundred three, section eighteen hundred three-a or this section of this article shall prevent the entry on the assessment roll of new property, additions to or improvements of existing property or formerly exempt property or the full or partial removal from the roll of property by reason of fire, demolition, destruction or new exemption.