N.Y. Civ. Serv. Law § 51

§ 51. Filling vacancies by open competitive examination. 1. Upon the\nwritten request of the appointing officer stating his reasons therefor,\nor on its own initiative, the state civil service department or\nappropriate municipal commission may determine to conduct an open\ncompetitive examination for filling a vacancy or vacancies instead of a\npromotion examination.\n 2. Except where the state civil service department or appropriate\nmunicipal commission finds that there are less than three persons\neligible for promotion in the promotion unit where the vacancy exists,\nor in the department, if such vacancy is not in a separate promotion\nunit, and except where the department or municipal commission determines\nto conduct an open competitive and a promotion examination\nsimultaneously, a notice of intention to conduct such open competitive\nexamination or a copy of the appointing officer's request for open\ncompetitive examination, as the case may be, shall be publicly and\nconspicuously posted in the offices of both the appointing officer and\nthe state civil service department or appropriate municipal commission\nand such request shall not be acted upon until said notice has been\nposted as aforesaid for a period of not less than fifteen days.\n 3. Any employee who believes that a promotion examination should be\nheld for filling such vacancy may submit to the state civil service\ndepartment or appropriate municipal commission his request, in writing,\nfor a promotion examination rather than an open competitive examination,\nstating the reasons why he believes it to be practicable and in the\npublic interest to fill the vacancy by promotion examination.\n