TrophyHunter is correct. Most peace officers as defined in CPL Article 210 must carry on their own private license under PL A400. This section specifically applies to NYC Firefighters, Westchester corrections, special police of a psych facility, NYS Thruway Authority, Marshalls of a city court (selecte cities), Parole Revocation Specialists, certain county park tangers, ASPCA officers, health inspectors, tax enforcement specialists, etc.
It is my understanding that a corrections officer must apply for a permit to carry outside the job, even when issued a permit for employment. This was communicated to me by Sheriff Dubois in Orange County.