Conn. Gen. Stat. § 27-153: Trial by civil authority.

(a) Under such regulations as may be prescribed by the Governor, a person subject to this code who is accused of an offense against civil authority may be delivered, upon request of such authority, to the civil authority for trial.

(b) When delivery under subsection (a) of this section is made to any civil authority of a person undergoing sentence of a court-martial, the delivery, if followed by conviction in a civil tribunal, interrupts the execution of the sentence of the court-martial, and the offender after having answered to the civil authorities for his offense shall, upon the request of competent military authority, be returned to military custody for the completion of his sentence.