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N.Y. Senate Rules § R5S6, under The Senate and Its Officers and Employees.

N.Y. Senate Rules § R5S6

§ 6. The Sergeant at Arms, under the jurisdiction of the Secretary, shall be the security officer of the Senate, and, except when absent in the discharge of his or her duties, shall be in constant attendance upon the sessions of the Senate and shall assign Assistant Sergeants at Arms to act as doorkeepers and, under the direction of the Presiding Officer, aid in enforcing order on the floor of the Senate, in the lobbies, and in the rooms adjoining the Senate Chamber, and also see that no person remains on the floor unless entitled to the privileges of the same. He or she shall also assist in maintaining order at hearings of the Senate and in that part of the Capitol and Legislative Office Building assigned to the use of the Senate and on sites in New York State where members are conducting the business of the Senate and security is deemed necessary by the Secretary.