(1) during the period beginning on the first of November, two thousand twelve and ending on the thirtieth of November, two thousand twelve, after inspection by the department, such building has been determined to be seriously damaged and unsafe to enter or occupy or completely demolished as a result of damage caused by the effects of the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve, and such determination has been indicated by a notation on such department's records and/or by the posting of a red placard warning on the building; or
(2) during the period beginning on the first of November, two thousand twelve and ending on the thirtieth of November, two thousand twelve, after inspection by the department, such building has been determined to require repairs or to have a restricted area and such determination has been indicated by a notation on such department's records and/or by the posting of a yellow sticker on the building, and during the period beginning on the first of December, two thousand twelve and ending on the twenty-eighth of December, two thousand twelve, after inspection by the department, such building has been determined to be seriously damaged and unsafe to enter or occupy or completely demolished as a result of damage caused by the effects of the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve, and such determination has been indicated by a notation on such department's records and/or by the posting of a red placard warning on the building. 4. Amount of rebate. a. The amount of the rebate to be paid by the commissioner of finance for eligible real property pursuant to subdivision one of this section shall be equal to two-thirds of the annual tax, multiplied by a fraction, the numerator of which is equal to that portion of the assessed valuation of the eligible real property that is attributable to the improvements on the property, and the denominator of which is equal to the total assessed valuation of the eligible real property. b. Except as provided in subdivision five of this section, for property held in the cooperative form of ownership, the amount of the rebate to be paid to the owner of a unit therein shall be equal to that proportion of the amount calculated under paragraph a of this subdivision that is attributable to such unit, as determined by the proportional relationship of the owner's share or shares of stock in the cooperative apartment corporation that owns such real property to the total outstanding stock of the cooperative apartment corporation. c. Eligible real property with no annual tax shall not be eligible for a rebate under this section. 5. Calculation of rebate for certain class one real property consisting of one family house structures situated on land held in cooperative ownership. a. Notwithstanding the provisions of subdivision four of this section, the amount of the rebate to be paid by the commissioner of finance to the owner of a building that was designated by the department of buildings in accordance with paragraph b of subdivision three of this section, that is located on eligible real property that is described in subparagraph (c) of paragraph class one of subdivision one of section eighteen hundred two of this chapter, shall be equal to two-thirds of the annual tax on the property of the cooperative development, (1) multiplied by a fraction, the numerator of which is equal to that portion of the assessed valuation of the eligible real property in the cooperative development that is attributable to the improvements on the property, and the denominator of which is equal to the total assessed valuation of the eligible real property in the cooperative development, and (2) multiplied by a second fraction, the numerator of which is equal to the number of buildings in the cooperative development that have been designated by the department of buildings in accordance with paragraph b of subdivision three of this section, and the denominator of which is the total number of buildings that were located in the cooperative development as of the twenty-eighth day of October, two thousand twelve, then (3) divided by the number of buildings in the cooperative development that have been designated by the department of buildings in accordance with paragraph b of subdivision three of this section. b. Eligible real property described in this subdivision with no annual tax shall not be eligible for a rebate under this section. 6. Mailing of rebate. a. The commissioner of finance shall mail the rebate authorized by this section to the person whose name appears on the records of the department of finance as the owner of the eligible real property or unit located therein on the thirtieth of October, two thousand twelve, at an address on the records of the department of finance as the address of such owner, and if no such address appears on the records of the department of finance, then to the address, if any, appearing in the latest assessment roll as the address of the owner of the eligible real property. Notwithstanding the previous sentence, if an owner has notified the United States postal service of a forwarding address for mail that would otherwise have been sent to any of the addresses described in the previous sentence, then the commissioner of finance may mail the rebate authorized by this section to such forwarding address. b. Notwithstanding paragraph a of this subdivision, with respect to any rebate to which an owner of a building that was designated by the department of buildings in accordance with paragraph b of subdivision three of this section that is located on eligible real property that is described in subparagraph (c) of paragraph class one of subdivision one of section eighteen hundred two of this chapter is entitled under this section, the commissioner of finance shall mail the rebate to the cooperative development of which the owner's property is a part, at the address on the records of the department of finance as the address of the cooperative corporation that is the owner of the land included in the cooperative development, and if no such address appears on the records of the department of finance, then to the address, if any, appearing in the latest assessment roll as the address of the owner of such land. Notwithstanding the previous sentence, if the cooperative corporation has notified the United States postal service of a forwarding address for mail that would otherwise have been sent to any of the addresses described in the previous sentence, then the commissioner of finance may mail the rebate authorized by this section to such forwarding address. 7. Recovery of erroneous rebate. If the commissioner of finance determines (a) that an owner who received a rebate was not entitled to a rebate under this section, or (b) that a rebate was paid or calculated in error under this section, the commissioner of finance shall recover or recalculate such rebate and the amount of the rebate or an amount equal to the difference between the rebate originally paid and the amount to which the owner was entitled shall be deducted from any refund or rebate otherwise payable to the owner, and any balance of such amount remaining unpaid shall be paid to the commissioner of finance no later than the due and payable date provided on a notice of the amount payable mailed by the commissioner of finance. Such amount payable shall constitute a tax lien on the real property owned by such owner as of the due and payable date provided on such notice, and, if not paid by such due and payable date, interest at the rate applicable to delinquent real property taxes on such property shall be charged and collected on such amount from the due and payable date provided on such notice to the date of payment, and such amount payable shall be enforceable as a tax lien in accordance with provisions of law relating to the enforcement of tax liens in any such city. 8. Rebate not deemed a refund. Any rebate authorized by this section to be paid by the commissioner of finance shall not be deemed to be a refund of a real property tax payment. 9. Overpayment. If, in any proceeding brought pursuant to article seven of the real property tax law, the assessed valuation of eligible real property is reduced for the fiscal year beginning on the first of July, two thousand twelve, and such reduction results in a return of overpayment of real property taxes paid with respect to such fiscal year, the amount of such overpayment shall be reduced by the amount of any rebate paid pursuant to this section. If such overpayment is returned before a rebate is paid pursuant to this section, the amount of any rebate paid pursuant to this section shall be reduced by the amount of such overpayment. 10. Rulemaking. The commissioner of finance shall be authorized to promulgate rules necessary to effectuate the purposes of this section.