Conn. Gen. Stat. § 52-159: Deposition may be used in another action.

The testimony of any witness, taken by deposition, in any civil action may be used in another civil action between the same parties, or their executors or administrators, and upon the same cause of action, to the same extent and as fully as though originally taken for use in such cause. The original deposition, when the authenticity of the same has been established, or a copy thereof, certified by the clerk of the court to which the original action was brought, shall be admitted in evidence as though originally taken for use in such cause.