Kan. Stat. § 22-4011
If any person who has been sentenced to death escapes and is not retaken before the time fixed for execution, it shall be lawful for any sheriff or other officer or person to rearrest and return the person to the custody of the secretary of corrections. Upon such return to custody, the secretary of corrections shall give notice thereof to the clerk of the supreme court. Upon receipt of such notice, the supreme court shall issue to the secretary of corrections a warrant under seal of the supreme court, commanding the secretary or a warden designated pursuant to K.S.A. 22-4001, and amendments thereto, to proceed to carry out the sentence of execution during the week designated by the supreme court which shall be carried into effect in the same manner as provided by statute for the execution of an original sentence of death. A copy of the warrant shall be delivered to the secretary of corrections and the clerk of the district court.
K.S.A. 22-4011