N.Y. Coop. Corp. Law § 63
Any member may bring charges against a director by filing them in writing with the secretary, together with a petition signed by five per centum of the members, requesting removal. The corporation may thereupon remove the director by the affirmative vote of three-fourths of the members voting thereon at a meeting promptly held after due notice in writing setting forth accurately the purpose for which such meeting is called, provided that at such meeting not less than ten per centum of the entire membership vote, personally or by mail. The director involved shall be given a copy of the charges reasonably in advance of the meeting, and he and the complainant shall have an opportunity at the meeting to be heard in person or by counsel and to present and cross examine witnesses.
In case the by-laws provide for election of directors by districts with primary elections in each district, then the petition for removal of a director must be signed by twenty per centum of the members residing in the district from which he was elected. The board of directors must call a special meeting of the members residing in that district to consider the removal of the director in the manner above provided; and, by a concurrent vote of a majority of the members of that district voting thereon, such director shall be removed from office.
N.Y. Coop. Corp. Law § 63