The Fourth Department determined an action to enforce a judgment against a party other than the judgment debtor (here a judgment creditor) under CPLR 5225 and 5227 is a proceeding for both legal and equitable relief for which a jury trial is not available:
“[T]he right to trial by jury is zealously protected in our jurisprudence and yields only to the most compelling circumstances” … . “Trial by jury in all cases in which it has heretofore been guaranteed by constitutional provision shall remain inviolate forever” (NY Const, art 1, § 2). “That guarantee extends to all causes of action to which the right attached at the time of adoption of the 1894 Constitution . . . Historically, however, actions at law were tried by a jury, [and] matters cognizable in equity were tried by the Chancellor. Even though the two systems have merged, vestiges of the law-equity dichotomy remain in the area relating to trial by jury” … .
Thus, the right to a jury trial “depends upon the nature of the relief sought” … . Under the CPLR, a jury trial is available in an action “in which a party demands and sets forth facts which would permit a judgment for a sum of money only” (CPLR 4101  [emphasis added]). Where a plaintiff joins legal and equitable causes of action in a complaint, it waives its right to a jury trial … . * * *
…[W]e conclude that enforcement of a judgment under CPLR 5225 and 5227 against a party other than the judgment debtor is an outgrowth of the “ancient creditor's bill in equity,” which was used after all remedies at law had been exhausted. We thus conclude that [the judgment creditor's] use of CPLR 5225 and 5227 in this case is in furtherance of both legal and equitable relief and, therefore, that [the judgment creditor] is not entitled to a jury trial on those combined legal and equitable claims … . Matter of Colonial Sur Co v Lakeview Advisors LLC, 2015 NY Slip Op 01002, 4th Dept 2-6-15