Bates v. Coe 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, John Bates, was held in a federal prison in the state of Missouri. Bates sought a writ of habeas corpus from the state court, claiming that he was being held in violation of his constitutional rights. 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 Bates v. Coe 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 Bates v. Coe, the United States Supreme Court was asked to decide whether a state court had jurisdiction over an action brought by a non-resident against another non-resident in which the cause of action arose outside of the state. The majority held that it did not have such jurisdiction and reversed the judgment of the lower court. Justice Field dissented from this opinion, arguing that states should be allowed to exercise their power to provide justice for all persons within their borders regardless of where they are domiciled or where any cause of action may arise. He argued that if states were prevented from exercising such authority then individuals would be deprived access to justice and denied due process rights guaranteed under both federal and state constitutions. Furthermore, he noted that there is no constitutional provision prohibiting states from providing remedies for wrongs committed outside its boundaries as long as those remedies do not conflict with federal law or interfere with interstate commerce.