In Crapo v. Kelly, the Supreme Court of the United States was asked to decide whether a state court had the authority to issue a writ of habeas corpus to a prisoner held in federal custody. The case arose when a prisoner, Crapo, was arrested and held in federal custody in the state of Massachusetts. Crapo's attorney sought a writ of habeas corpus from the state court, arguing that the federal court had no jurisdiction over the matter. 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 in this case. The Court reasoned that the federal government had exclusive jurisdiction over matters involving federal prisoners, and that the state court had no authority to interfere in such matters. The Court also noted that the writ of habeas corpus was a remedy available only to those held in state custody, and not to those held in federal custody. In its decision, the Supreme Court affirmed the principle that the federal government has exclusive jurisdiction over matters involving federal prisoners. The Court also held that the writ of habeas corpus was not available to those held in federal custody. This decision has been cited in numerous subsequent cases involving the rights of federal prisoners.

In Crapo v. Kelly, the Supreme Court was asked to decide whether a state court had jurisdiction over an action brought by a non-resident plaintiff against a resident defendant. The majority opinion held that it did not have jurisdiction and dismissed the case. However, Justice Field dissented from this decision on two grounds: first, he argued that under the Constitution's Full Faith and Credit Clause, states are required to give full faith and credit to judgments of other states; second, he argued that if Congress has granted exclusive original jurisdiction in certain cases to federal courts then such authority should be respected even when there is concurrent state court jurisdiction. He concluded his dissent with an argument for judicial restraint - namely that since no constitutional question was raised or decided in this case then it should be left up for determination by Congress rather than the judiciary.