A summary inquiry into any alleged violation or neglect of duty in relation to the property, government or affairs of the city may be conducted under an order to be made by any justice of the supreme court in the first, second or eleventh judicial district on application of the mayor, the comptroller, the public advocate, any five council members, the commissioner of investigation or any five citizens who are taxpayers, supported by affidavit to the effect that one or more officers, employees or other persons therein named have knowledge or information concerning such alleged violation or neglect of duty. Such inquiry shall be conducted before and shall be controlled by the justice making the order or any other justice of the supreme court in the same district. Such justice may require any officer or employee or any other person to attend and be examined in relation to the subject of the inquiry. Any answers given by a witness in such inquiry shall not be used against such witness in any criminal proceeding, except that for all false answers on material points such witness shall be subject to prosecution for perjury. The examination shall be reduced to writing and shall be filed in the office of the clerk of such county within the first, second or eleventh judicial district as the justice may direct, and shall be a public record.