N.Y. Correct. Law § 614

§ 614. Care and support of civil prisoner. A person arrested, by\nvirtue of an order of arrest, in an action or special proceeding brought\nin a court of record; or of an execution issued upon a judgment rendered\nin a court of record; or surrendered in exoneration of his bail; must be\nsafely kept in custody, in the manner prescribed by law, and, except as\nherein otherwise provided, at his own expense, until he satisfies the\njudgment rendered against him, or is discharged according to law. In any\ncounty, if a prisoner, actually confined in jail, makes oath before the\nsheriff, jailer, or deputy-jailer, that he is unable to support himself\nduring his imprisonment, his support is a county charge.\n