What is Capias Ad Respondendum?

Legal Definition
In the common law legal systems, capias ad respondendum (Latin: "that you may capture [him] in order for him to reply") is or was a writ issued by a court to the sheriff of a particular county to bring the defendant, having failed to appear, to answer a civil action against him.

Under the American legal system, this writ was replaced by the practice of serving process directly to the person of the defendant in order to compel him to appear before the court to establish in personam jurisdiction over him according to his rights under the Due Process Clause of the Fourteenth Amendment. "But now that the capias ad respondendum has given way to personal service of summons or other form of notice, due process requires only that in order to subject a defendant to a judgment in personam, if he be not present within the territory of the forum, he have certain minimum contacts with it such that the maintenance of the suit does not offend 'traditional notions of fair play and substantial justice.'"

In the United Kingdom, this writ was abolished by the Crown Proceedings Act 1947 which came into effect on January 1, 1948.
-- Wikipedia
Legal Definition
Practice. A writ commanding the sheriff, or other proper officer, to "take the body of the defendant and to keep the same to answer, ad respondendum, the plaintiff in a plea," &c. The amount of bail demanded ought to, be endorsed on the writ.

2. A defendant arrested upon this writ must be committed to prison, unless he give a bail bond (q. v.) to the sheriff. In some states, (as, until lately, in Pennsylvania,) it is the practice, when the defendant is liable to this process, to indorse on the writ, No bail required in which case he need only give the sheriff, in writing, an authority to the prothonotary to enter his appearance to the action, to be discharged from the arrest. If the writ has been served, and the defendant have not given bail, but remains in custody, it is returned C. C., cepi corpus; if he have given bail, it is returned C. C. B. B., cepi corpus, bail bond; if the defendant's appearance have been accepted, the return is, " C. C. and defendant's appearance accepted." According to the course of the practice at common law, the writ bears teste, in the name of the chief justice, or presiding judge of the court, on some day in term time, when the judge is supposed to be present, not being Sunday, and is made returnable on a regular return day. 1 Penna. Pr. 36; 1 Arch. Pr. 67.
-- Bouviers Law Dictionary
Legal Definition
A judicial writ, (usually simply termed a "capias,") by which actions at law were frequently commenced; and which commands the sheriff to take the defendant, and him safely keep, so that he may bave his body before the court on a certain day, to answer the plaintiff in the action. 3 Bl. Comm. 282; 1 Tidd, Pr. 128. The name of this writ is commonly abbreviated to oa. resp.
-- Black's Law Dictionary
Legal Definition
A writ for the arrest of the defendant in a civil action.
-- Ballentine's Law Dictionary