Relfe v. Rundle was a United States Supreme Court case that dealt with the issue of whether a state court had the authority to issue a writ of habeas corpus to a prisoner who was being held in a federal prison. The case arose when a prisoner, Relfe, was held in a federal prison in the state of Mississippi. Relfe sought a writ of habeas corpus from the state court, claiming that he was being held in violation of the Constitution. The state court granted the writ, and the federal government appealed the decision to the Supreme Court. The Supreme Court held that the state court did not have the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The Court reasoned that the writ of habeas corpus was a federal remedy, and that the state court did not have the power to interfere with the federal government's authority to imprison individuals. The Court also noted that the writ of habeas corpus was a remedy that could only be used to challenge the legality of a person's detention, and not to challenge the conditions of the detention. The Court's decision in Relfe v. Rundle established that state courts do not have the authority to issue writs of habeas corpus to prisoners held in federal prisons. This decision has been cited in numerous subsequent cases, and has been used to support the principle that state courts cannot interfere with the federal government's authority to imprison individuals.

In Relfe v. Rundle, the Supreme Court was asked to decide whether a state court judgment could be enforced against an individual who had not been served with process in that action. The majority of the Court held that it could not, as service of process is necessary for a valid judgment to be entered and enforced by another jurisdiction. Justice Field dissented from this opinion, arguing that due process does not require personal service when there is sufficient evidence before the court showing actual notice or knowledge of proceedings on behalf of the defendant. He argued further that if such proof exists then enforcement should be allowed regardless of any technical defects in service which may have occurred during litigation. In his view, allowing judgments based on constructive notice would promote justice and prevent frauds upon individuals who are unaware they are being sued until after a decision has already been rendered against them.