Conn. Gen. Stat. § 12-365

(b) If no administration has been granted upon the estate of the transferor because of the fact that the transferor died without leaving property which could pass by his will or by the laws of this state relating to descent and distribution, the court of probate for the district within which the transferor resided at the date of his death or, if the transferor died a nonresident of this state, the court of probate for the district within which the real estate or tangible personal property is situated, may, upon its own motion or upon the written application of the Commissioner of Revenue Services, the transferee or any party in interest appoint an administrator for the purpose of determining and collecting the tax due under the provisions of this chapter. Such fiduciary shall have the same duties and powers relating to the filing of a return and relating to the collection and payment of any such tax as if such property had belonged to the transferor at the date of his death.