Conn. Gen. Stat. § 49-24: Court may foreclose lien or mortgage on land by sale or market sale.

All liens and mortgages affecting real property may, on the written motion of any party to any suit relating thereto, be foreclosed (1) by a decree of sale instead of a strict foreclosure at the discretion of the court before which the foreclosure proceedings are pending, or (2) with respect to mortgages, as defined in section 49-24a, that are a first mortgage against the property, by a judgment of foreclosure by market sale upon the written motion of the mortgagee, as defined in section 49-24a, and with consent of the mortgagor, as defined in section 49-24a, in accordance with sections 49-24a to 49-24g, inclusive, and sections 49-26 to 49-28, inclusive.