Cramer v. Arthur was a United States Supreme Court case that addressed the issue of whether a state court could issue a writ of mandamus to compel a county auditor to issue a tax deed. The case was brought by the plaintiff, Cramer, who sought to compel the defendant, Arthur, to issue a tax deed for a piece of property in the state of Ohio. The Supreme Court held that the state court did not have the authority to issue a writ of mandamus to compel the county auditor to issue a tax deed. The Court reasoned that the power to issue a tax deed was a power vested in the county auditor by the state legislature, and that the state court did not have the authority to interfere with the county auditor's exercise of that power. The Court further held that the state court could not issue a writ of mandamus to compel the county auditor to issue a tax deed because the county auditor was not a ministerial officer, and thus was not subject to the writ of mandamus. In conclusion, the Supreme Court held that the state court did not have the authority to issue a writ of mandamus to compel the county auditor to issue a tax deed. The Court reasoned that the power to issue a tax deed was a power vested in the county auditor by the state legislature, and that the state court did not have the authority to interfere with the county auditor's exercise of that power.

In Cramer v. Arthur, the Supreme Court was tasked with determining whether a state court had jurisdiction to issue an injunction against a party who had been found guilty of contempt in another state. The majority opinion held that the lower court did not have jurisdiction and thus could not issue such an injunction. Justice Field dissented from this decision, arguing that it would be unjust for one state's courts to lack authority over matters which were initiated within its own borders. He argued further that if states are unable to exercise their power over those who violate their laws, then they will become powerless and unable to protect themselves or their citizens from wrongdoers. Furthermore, he noted that since the defendant was already found guilty of contempt in another state, there should be no reason why he should not also face punishment in his home state as well.