N.Y. Comp. Codes R. & Regs. tit. 20, § 151.11
(1) Where one or both spouses die during the year and would have been entitled to file a joint New York State personal income tax return had they lived, a joint New York State personal income tax return may be made, on form IT-200, form IT-201 or form IT-203, if:
Tax Law, § 651(c)
(a) General.
In general, the same rules for filing New York State personal income tax returns apply to a decedent as in the case of any other taxpayer. The executor or administrator of the estate of a taxpayer who died during the taxable year, or any other person charged with the property of such a decedent, must make and file a New York State personal income tax return for him on the form (IT-200, IT-201 or IT-203) which would have been appropriate had he lived. For the decedent's taxable year which ends with the date of his death, such return will cover the period during which he was alive.
(b) Joint New York State personal income tax return after death.