Conn. Gen. Stat. § 52-252: Costs for nonappearance of party giving notice of deposition.

When a notice is given to an adverse party or his known agent or attorney, or left at his usual place of abode, that a deposition will be taken at a certain time and place, and the adverse party, or his agent or attorney, appears at such time and place for that purpose and the party giving notice does not appear or for any reason does not take the deposition at such time and place, costs shall be allowed to the adverse party at the discretion of the court before which the action is pending.