A Tennessee Civil Warrant is a court order issued by a judge or magistrate in the state of Tennessee, and it authorizes law enforcement to take a person into custody and bring them before a court. There are two types of Tennessee Civil Warrants: a capitalas” warrant and a “writ of execution.capitalcapias warrant is issued when a defendant fails to appear in court to answer a complaint, while a writ of execution is issued when a judgment has been entered against a party and the court wants to collect payment from the defendant. Both types of Tennessee Civil Warrants allow law enforcement to arrest the defendant and bring them before a court.