Conn. Gen. Stat. § 6-32: Duties. Cost of serving a civil protection order.

(a) Each state marshal shall receive each process directed to such marshal when tendered, execute it promptly and make true return thereof; and shall, without any fee, give receipts when demanded for all civil process delivered to such marshal to be served, specifying the names of the parties, the date of the writ, the time of delivery and the sum or thing in demand. If any state marshal does not duly and promptly execute and return any such process or makes a false or illegal return thereof, such marshal shall be liable to pay double the amount of all damages to the party aggrieved.

(b) A civil protection order constitutes civil process for purposes of the powers and duties of a state marshal. The cost of serving a civil protection order issued pursuant to section 46b-16a shall be paid by the Judicial Branch in the same manner as the cost of serving a restraining order issued pursuant to section 46b-15, and fees and expenses associated with the serving of a civil protection order shall be calculated in accordance with subsection (a) of section 52-261.