(b) A local law imposing such a tax shall be effective only during the period that each of the school districts partly within and partly without such city, by a majority vote of the whole number of its school authorities, shall impose an identical tax, at the same uniform rate, within that part of its territorial limits outside of such city. Such school authorities are hereby authorized and empowered to impose such tax so as to be effective only during the period when the tax imposed by the city on areas of school districts within the city shall be effective. Taxes so imposed by such a city and by such school districts shall be administered and collected by the state tax commission as provided in subpart B of part III of this article.

(c) All actions taken by majority votes of school authorities pursuant to this section shall be deemed resolutions under this article and shall be official records of the school districts in which they are taken.

(d) A local law or resolution imposing any tax pursuant to this section, increasing or decreasing the rate of such tax, repealing or suspending such tax or providing for the credit or refund described in clause six of subdivision (a) of section eleven hundred nineteen of this chapter must go into effect only on one of the following dates: March first, June first, September first or December first, subject to further requirement as to effective date provided for in subdivision (b) of this section; provided, that a local law or resolution providing for a refund or credit described in subdivision (d) of section eleven hundred nineteen of this chapter or repealing such provision so provided must go into effect only on March first, subject to further requirement as to effective date provided for in subdivision (b) of this section. No such local law or resolution shall be effective unless a certified copy of such local law or resolution is mailed by registered or certified mail to the commissioner at the commissioner's office in Albany at least ninety days prior to the date it is to become effective. However, the commissioner may waive and reduce such ninety-day minimum notice requirement to a mailing of such certified copy by registered or certified mail within a period of not less than thirty days prior to such effective date if the commissioner deems such action to be consistent with the commissioner's duties under section twelve hundred fifty of this article and the commissioner acts by resolution. Where the restriction provided for in section twelve hundred twenty-three of this article as to the effective date of a tax and the notice requirement provided for therein are applicable and have not been waived, the restriction and notice requirement in section twelve hundred twenty-three of this article shall also apply.

(e) Certified copies of any local law or resolution described in subdivision (d) of this section shall also be filed with the city clerk, state department of education, the secretary of state and the state comptroller within five days after the date it is enacted. Certified copies of any other local law or resolution enacted pursuant to this section shall be filed with the state tax commission, the city clerk, the state department of education, the secretary of state and the state comptroller within five days after the date it is enacted.