When the parties in any action pending before the Supreme Court, or their attorneys, sign and file with the clerk an agreement as to the judgment which shall be rendered therein, the clerk may enter judgment in the action upon the written order of the Chief Justice or presiding judge of the Supreme Court.
Conn. Gen. Stat. § 51-208
(1949 Rev., S. 7682; P.A. 82-248, S. 109.)