Conn. Gen. Stat. § 12-402: Tax to be paid by executor or administrator.

So far as is practicable, the tax shall be paid by the executor or administrator as such out of the estate before its distribution, unless the decedent's will, if any, otherwise directs. When any property required to be included in the gross estate does not come into the possession of the executor or administrator as such, he shall recover from whoever is in possession or from the persons interested in the estate the proportionate amount of such tax payable by the persons interested in the estate with which such persons are chargeable under the provisions of this chapter, and the probate judge may by order direct the payment of such amount by such person to the executor or administrator.