N.Y. Town Law § 156

§ 156. Effect of resignation. Any member of such department who shall\nresign shall be eligible for reinstatement in the same police force or\npolice department or in any other police force or police department to\nwhich he was eligible for transfer at the time of his resignation,\nprovided such reinstatement occurs within one year of the date of\nresignation and further provided that such application for reinstatement\nshall be made in writing within such one year period.\n