Conn. Gen. Stat. § 52-343: Death of garnishee pending attachment.

If any executor, administrator or trustee, in whose hands any debt, legacy or distributive share has been so attached, dies or is removed pending the proceedings either on the original writ or on the scire facias, upon proper suggestion being made upon the record such proceedings may be continued against the survivor, or his successor in such trust, as the case may be, in the same manner as they might otherwise have been against the original garnishee or garnishees.