New York Consolidated Laws, Domestic Relations Law - DOM § 172. Co-respondent as party

1. In an action brought to obtain a divorce on the ground of adultery the plaintiff or defendant may serve a copy of his pleading on a co-respondent named therein.  At any time within twenty days after such service, the co-respondent may appear to defend such action so far as the issues affect him.  If no such service be made, then at any time before the entry of judgment a co-respondent named in any of the pleadings may make a written demand on any party for a copy of a summons and a pleading served by such party, which must be served within ten days thereafter, and he may appear to defend such action so far as the issues affect him.

2. In an action for divorce where a co-respondent has appeared and defended, in case no one of the allegations of adultery controverted by such co-respondent shall be proven, such co-respondent shall be entitled to a bill of costs against the person naming him as such co-respondent, which bill of costs shall consist only of the sum now allowed by law as a trial fee, and disbursements.