N.Y. CPLR 3031
An action may be commenced without the service of a summons, or may be continued after the service of a summons, without pleadings, by the filing of a statement, signed and acknowledged by all the parties or signed by their attorneys, specifying plainly and concisely the claims and defenses between the parties and the relief requested. Signing constitutes a certificate that the issues are genuine, and such filing, together with a note of issue, to be filed at the same time, shall constitute the joinder of issues in the action. The procedure in any action commenced under this section shall constitute "the New York Simplified Procedure for Court Determination of Disputes" and it shall be sufficient so to identify the procedure in any contract or other document referring to it. A submission of a controversy under this procedure shall constitute a waiver by the parties of the right to trial by jury.
N.Y. CPLR 3031