N.Y. Comp. Codes R. & Regs. tit. 20, § 17-1.4 – 52-53-week fiscal year taxpayers.

(a) A taxpayer which reports on the basis of a 52-53-week accounting period for Federal income tax purposes must report on the same basis for purposes of article 32 of the Tax Law. A 52-53-week period must end on the same day of the week each year and end always on whatever date that day of the week last occurs in a calendar month, or on whatever date that day of the week falls which is nearest the last day of a calendar month.
(b) If a 52-53-week accounting period is used and the period starts within seven days from the first day of any calendar month, the taxable year will be deemed to have begun on the first day of such calendar month. If a 52-53-week accounting period ends within seven days from the last day of any calendar month, the taxable year will be deemed to have ended on the last day of such month.
(c) If a taxpayer uses a 52-53-week accounting period for Federal income tax purposes and becomes subject to tax under article 32 of the Tax Law, the taxpayer may be required to file returns for two taxable years during an accounting period for which one Federal return is required. For example, a banking corporation organized in New York State receives its corporate franchise on Monday, October 29, 1984. The corporation uses a 52-53-week accounting period ending on the Saturday nearest the last day of October for Federal income tax purposes. The 52-53-week accounting period for which the corporation computes its tax for Federal income tax purposes begins October 28, 1984 and ends Saturday, November 2, 1985. For purposes of article 32 of the Tax Law, the period from October 29, 1984 to October 31, 1984, inclusive, is deemed to be the first period for which a return is due and a tax payable. The next taxable period is deemed to be from November 1, 1984 to October 31, 1985 and is based on the accounting period ending November 2, 1985.