N.Y. DOM Law § 172

§ 172. Co-respondent as party. 1. In an action brought to obtain a\ndivorce on the ground of adultery the plaintiff or defendant may serve a\ncopy of his pleading on a co-respondent named therein. At any time\nwithin twenty days after such service, the co-respondent may appear to\ndefend such action so far as the issues affect him. If no such service\nbe made, then at any time before the entry of judgment a co-respondent\nnamed in any of the pleadings may make a written demand on any party for\na copy of a summons and a pleading served by such party, which must be\nserved within ten days thereafter, and he may appear to defend such\naction so far as the issues affect him.\n 2. In an action for divorce where a co-respondent has appeared and\ndefended, in case no one of the allegations of adultery controverted by\nsuch co-respondent shall be proven, such co-respondent shall be entitled\nto a bill of costs against the person naming him as such co-respondent,\nwhich bill of costs shall consist only of the sum now allowed by law as\na trial fee, and disbursements.\n