(a) Notwithstanding the provisions of section 45a-727, in the case of a child sought to be adopted by a stepparent, the Court of Probate may waive all requirements of notice to the Commissioner of Children and Families and shall waive, unless good cause is shown for an investigation and report, all requirements for investigation and report by the Commissioner of Children and Families or by a child-placing agency. Upon receipt of the application and agreement, the Court of Probate may set a day for a hearing upon the agreement and shall give reasonable notice of the hearing to the parties to the agreement and to the child, if over twelve years of age.

      (b) At the hearing the court may deny the application, enter a final decree approving the adoption if it is satisfied that the adoption is in the best interests of the child, or, for good cause shown, order an investigation by the Commissioner of Children and Families or a child-placing agency.