Coe v. Errol was a United States Supreme Court case that addressed 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, William Coe, was held in a federal prison in New York. Coe 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 prerogative, and that the state court did not have the authority to interfere with the federal government's power to imprison individuals. The Court also noted that the writ of habeas corpus was a fundamental right, and that the state court should not be allowed to interfere with the federal government's power to protect the rights of individuals. In conclusion, 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 prerogative, and that the state court did not have the authority to interfere with the federal government's power to imprison individuals. The Court also noted that the writ of habeas corpus was a fundamental right, and that the state court should not be allowed to interfere with the federal government's power to protect the rights of individuals.

In the case of Coe v. Errol, the Supreme Court was asked to decide whether a New Hampshire statute that allowed for an appeal from a decision by a single justice of the state's supreme court was constitutional. The majority opinion held that it was not, as it violated Article III of the Constitution which requires all cases in federal courts to be heard by at least three judges. Justice Field dissented on this point and argued that states should have some flexibility when deciding how their own judicial systems are structured and operated. He noted that there had been no challenge to similar statutes in other states and thus concluded that such laws were consistent with both state sovereignty and Article III’s requirement for multiple judges hearing cases in federal courts. In addition, he argued against what he saw as an overly broad interpretation of Article III by noting its language only applied specifically to “the judicial power” rather than any action taken within a state court system or legislature.