N.Y. Real Prop. Acts. Law § 915
The interlocutory judgment shall determine the right, share or interest of each party in the property, as far as the same has been ascertained. Where the property or any part thereof is so circumstanced that a partition thereof cannot be made without great prejudice to the owners, the interlocutory judgment, except as otherwise expressly prescribed in this article, shall direct that the property or the part so circumstanced be sold at public auction. Otherwise, an interlocutory judgment in favor of the plaintiff shall direct that partition be made between the parties according to their respective rights, shares and interests and shall designate three reputable and disinterested freeholders as commissioners to make the partition so directed.
N.Y. Real Prop. Acts. Law § 915