Smith v. Cockrill 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 held in a federal prison. The case arose when a prisoner, Smith, was held in a federal prison in Tennessee and sought a writ of habeas corpus from the state court. 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 the writ of habeas corpus. The Court reasoned that the writ of habeas corpus was a federal power, 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 this right. The Court's decision in Smith v. Cockrill established that the state court did not have the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. This decision has been cited in numerous cases since then, and has been used to support the idea that the federal government has the power to protect the fundamental right of habeas corpus.

In Smith v. Cockrill, the Supreme Court was asked to decide whether a state court had jurisdiction over a case involving citizens of different states. The majority opinion held that the state court did have jurisdiction and could proceed with the case as it saw fit. However, Justice Field dissented from this opinion on two grounds: firstly, he argued that under Article III of the Constitution, federal courts were given exclusive original jurisdiction in cases between citizens of different states; secondly, he argued that even if there was concurrent jurisdiction between both federal and state courts in such cases (which he believed there wasn't), Congress had not yet passed any laws granting such power to state courts. Therefore, according to Justice Field's dissent, only federal courts should be allowed to hear these types of cases until Congress passes legislation explicitly allowing for concurrent jurisdiction between both levels of government.