N.Y. Comp. Codes R. & Regs. tit. 22, § 25.20
(2) Whenever a vacancy exists in a competitive class position and an open competitive examination does not result in an eligible list containing the names of at least three persons willing to accept appointment, a person may be nominated for noncompetitive examination for such position. If such nominee shall be certified by the Chief Administrator as qualified, he or she may be appointed to fill such vacancy. The Chief Administrator also may designate an eligible list as a continuing eligible list in accordance with section 25.18 of this Part.
(b) Prohibition against out-of-title work.
No person shall be appointed, promoted or employed under any title not appropriate to the duties to be performed and, except upon assignment by proper authority during the continuance of a temporary emergency situation, no person shall be assigned to perform the duties of any position unless he or she has been duly appointed, promoted, transferred, reassigned or reinstated to such position in accordance with the provisions of this Part. No credit shall be granted in a promotion examination for out-of-title work.
(c) Trainee appointments.
The Chief Administrator may require that permanent appointments or promotions to designated positions shall be conditioned upon the satisfactory completion of a term of service as a trainee in such a position or in an appropriate, lower, training title or the completion of specified training or academic courses, or both. Upon the satisfactory completion of such training term, and of specified courses if required, an appointee shall be entitled to full permanent status in the position for which appointment was made. Any appointment hereunder shall be subject to such probationary period as is prescribed in this Part. The employment of such person may be discontinued at the end of the term of training service if his or her conduct, capacity or fitness is not satisfactory, or at any time if he or she fails to pursue or continue satisfactorily such training or academic courses as may be required.
(d) Seasonal positions.
(a) Appointment or promotion from eligible lists.