N.Y. Second Class Cities Law § 34
The common council shall determine the rules of its own proceedings and be the judge of the election, returns and qualifications of its members. Its meetings shall be public and its records open to public inspection, and a majority of all its members shall constitute a quorum to do business. The common council may compel the attendance of absent members at any meeting properly called, and may punish or expel a member for disorderly conduct, for a violation of its rules or for official misconduct, or declare his seat vacant by reason of absence, provided such absence has continued for the space of two months; but no expulsion shall take place and no vacancy on account of absence be declared except by the vote of three-fourths of all the members of the common council, nor until the delinquent member has had an opportunity to be heard in his defense. All appointments or designations made by the common council shall be determined upon a vote taken by a roll call of its members, and a statement of the choice of each member or the yeas and nays, if any, shall be entered upon the journal.
N.Y. Second Class Cities Law § 34