In Bostwick v. Brinkerhoff, the United States Supreme Court was asked to decide whether a state court had the authority to issue a writ of mandamus to compel a county auditor to issue a tax deed. The case arose when the plaintiff, Bostwick, purchased a piece of land from the county auditor, Brinkerhoff, and paid the taxes due on the property. However, Brinkerhoff refused to issue a tax deed for the property, claiming that the taxes had not been paid in full. Bostwick then sought a writ of mandamus from the state court, which ordered Brinkerhoff to issue the deed. Brinkerhoff appealed the decision to the Supreme Court, arguing that the state court did not have the authority to issue the writ. The Supreme Court held that the state court did have the authority to issue the writ of mandamus. The Court reasoned that the writ was necessary to protect Bostwick's rights, as he had paid the taxes due on the property and was entitled to a deed. The Court also noted that the writ was necessary to ensure that the county auditor fulfilled his duties in accordance with the law. As such, the Court held that the state court had the authority to issue the writ of mandamus and affirmed the decision of the lower court.

In Bostwick v. Brinkerhoff, the Supreme Court was tasked with deciding whether a New York statute that allowed for an appeal from a judgment of foreclosure to be taken directly to the state's highest court was constitutional. The majority opinion held that it did not violate Article III of the Constitution and thus could stand as written. Justice Field dissented, arguing that this interpretation violated both Article III and Article IV by allowing one party in a case to bypass lower courts without any opportunity for review or consideration of their arguments. He further argued that such an action would lead to unequal protection under law since some parties may have access to higher courts while others do not due solely based on where they live or what type of case is being heard. Ultimately, he concluded that if Congress had intended such an outcome then they should have explicitly stated so in either article rather than leaving it up for judicial interpretation which could potentially lead to arbitrary decisions regarding who has access and who does not when appealing judgments from lower courts.