N.Y. Indian Law § 52
If any party shall fail to comply with, or fulfil the directions or finding of the peacemakers in any matter heard or determined by them in pursuance of law, within the time fixed by such determination, the party in whose favor such determination may be, shall be entitled to recover the amount awarded to him, by such determination with costs, in an action in justice's court before any justice of the peace of the county in which such reservation or a part thereof is situated, in which action, a copy of the record of such determination, certified to by said clerk, shall be conclusive evidence of the right of recovery, and of the amount of such recovery, and executions shall be awarded to enforce the collection of the judgment obtained thereon in the same manner and with the like effect as against white persons, and the property and person of the defendant in such action shall be liable to seizure and sale or imprisonment, as in like cases against white persons. In case the action or proceeding is one not within the jurisdiction of justice's courts, the application may be made to a court having jurisdiction of actions of the same nature.
N.Y. Indian Law § 52