N.Y. Comp. Codes R. & Regs. tit. 9, § 560.3
(f) Terminations of the services of probationers pursuant to the Civil Service Law are not reviewable by the grievance appeals board except where the petitioner presents prima facie proof to the board that the decision of the appointing officer may have been arbitrary or capricious. In such cases, the board may:
(a)