N.Y. Comp. Codes R. & Regs. tit. 22, § 25.14
The Chief Administrator of the Courts may conduct an open competitive examination for filling a vacancy or vacancies instead of a promotion examination. Any employee or employee organization may submit to the Chief Administrator a request, in writing, for a promotion examination, rather than an open competitive examination, stating the reasons why it is practicable and in the public interest to fill the vacancy by promotion examination.