(b) A local law adopted pursuant to paragraph (a) of this subdivision shall remain in full force and effect unless rescinded by a subsequent local law which shall be subject to the same referendum and notice provisions.

(c) Upon receipt of the notice of the enactment of the village local law as provided in paragraph (a) of this subdivision, the assessor of the applicable town or county shall thereafter annually prepare a copy of that part of the final town or county assessment roll applicable to the village, which copy shall conform to the applicable part of the town or county assessment roll and assessments made or approved by the commissioner for the village portion of the town or county assessment roll pursuant to title two-A and two-B of article four, title two of article five, and article six of this chapter, shall be the assessments for village purposes. The taxable status date of the town or county shall control for village purposes. The town or county assessor shall deliver such copy to the board of trustees of the village no later than five days after the completion and filing of the final town or county assessment roll. The expense of preparing and furnishing such duplicate part of the town or county assessment roll shall be a village charge to be raised and collected as are other village charges. In lieu of the duplicate copy of the appropriate part of the town or county assessment roll, upon agreement between the town or county assessor and the village board of trustees, the assessor may provide a data file, as that term is defined in section fifteen hundred eighty-one of this chapter, and a summary of the information contained therein, including the number of parcels and the total assessed value thereof. Nothing contained herein shall relieve the village authorities from full responsibility for ascertaining whether real property is within the village boundaries.

(d) When a village, which has enacted a local law as provided in paragraph (a) of this subdivision, is located in two or more towns, the village board of trustees shall annually secure from the commissioner a statement of the latest state equalization rates established by such commissioner for each town in which such village is partially situated. The state equalization rate to be furnished by the commissioner shall be the rate established by the commissioner for the assessment roll on which village 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 change in the level of assessment has occurred between such preceding roll and the roll on which taxes are to be levied, a special equalization rate shall be established. In all cases, in any given village, the state equalization rates or special equalization rates to be furnished by the commissioner to the village shall have the same full value standard. The board of trustees shall determine the full valuation of the real property of each part of the towns included in such village by dividing the total assessed valuation of the real property in the appropriate part of each town by the state equalization rate established for such town. The village board of trustees shall also determine what proportion of the tax to be levied in the village shall be levied upon each part of a town included in such village by dividing the sum of the full valuation of taxable real property in the appropriate part of each town by the total full valuation of real property in the village. Such proportions shall be expressed to the nearest exact ten thousandths and the village board of trustees of such village shall levy such a proportion of any tax to be raised in the village during the current fiscal year upon each part of a town included in such village as shall have been determined by the board of trustees. A new proportion shall be determined for each fiscal year thereafter by the board of trustees in accordance with the provisions of this section by the use of the latest state equalization rates. The provisions of this paragraph shall not apply to a village which has adopted the provisions of section nineteen hundred three-a of this chapter. 4. Newly incorporated villages. A village which, on or after the first day of January, nineteen hundred ninety-five, is incorporated pursuant to article two of the village law shall be a non-assessing unit village as provided in paragraph (a) of subdivision three of this section. Such a village may, however, enact a local law, subject to permissive referendum as provided in article nine of the village law, to become an assessing unit as prescribed in subdivision one of this section. Notwithstanding the foregoing provisions of this subdivision, a village incorporated on or after the first day of January, nineteen hundred ninety-five, which is located in two or more towns having different taxable status dates, shall be an assessing unit as prescribed in subdivision one of this section. 5. Coterminous towns-villages. A village which embraces the entire territory of a town and is subject to the provisions of section 17-1722-a of the village law is not subject to the provisions of this section.