N.Y. County Law § 831
The legislature of the county of Dutchess may authorize the purchase of burial plots and provide for marker settings and perpetual care and maintenance of such plots in one or more of the cemeteries of the county of Dutchess for deceased veterans, who, at the time of death, were residents of the county of Dutchess and who (i) were discharged from the armed forces of the United States either honorably or under honorable circumstances, or (ii) had a qualifying condition, as defined in section one of the veterans' services law, and received a discharge other than bad conduct or dishonorable, or (iii) were a discharged LGBT veteran, as defined in section one of the veterans' services law, and received a discharge other than bad conduct or dishonorable. The expense thereof shall be a county charge.
N.Y. County Law § 831