Conn. Gen. Stat. § 48-23

When, under the provisions of any statute authorizing the condemnation of land in the exercise of the right of eminent domain, an appraisal of damages has been returned to the clerk of the Superior Court, as provided by law, and when the amount of appraisal has been paid or secured to be paid or deposited with the State Treasurer, as provided by law, any judge of the Superior Court may, upon application and proof of such payment or deposit, order such clerk to issue an execution commanding a state marshal to put the parties entitled thereto into peaceable possession of the land so condemned.