Conn. Gen. Stat. § 3-10f: Flying flags at half-staff.

(a) In the event of the death of a present or former principal figure of state government or of a member of the armed forces, as defined in section 27-103, who is from Connecticut and dies in the line of duty, the Governor may proclaim that the national flag be flown at half-staff. When such proclamation is issued, all state government buildings, offices, public schools and military bases shall fly the national flag and the state flag at half-staff.

(b) In the event of the death of a state official or prominent citizen, the Governor may proclaim that the state flag be flown at half-staff. When such proclamation is issued, all state government buildings, offices, public schools and military bases shall fly the state flag at half-staff.