In the 1935 case of Wisconsin v. Michigan, the U.S. Supreme Court was asked to resolve a dispute over territory and jurisdiction between the two states. The conflict centered around an area known as the "Quinnesec Falls" on Menominee River, which forms part of the boundary between Wisconsin and Michigan's Upper Peninsula. Both states claimed sovereignty over this region due to ambiguities in their original territorial charters dating back to when they were admitted into Union. Wisconsin argued that it had been exercising jurisdiction without challenge for many years, while Michigan contended that historical documents clearly placed Quinnesec Falls within its boundaries. The Supreme Court ruled in favor of Michigan after examining various maps, treaties with Native American tribes, acts of Congress related to statehood admissions and other historical records relevant to determining state lines at different points in time. The court found these sources collectively indicated that Quinnesec Falls was intended by Congress to be part of Michigan when both states were admitted into Union. This decision affirmed federal courts' authority under Article III Section 2 Clause 2 (Original Jurisdiction) of U.S Constitution - allowing them adjudicate disputes involving two or more States directly rather than going through lower courts first.

In the dissenting opinion for Wisconsin v. Michigan, 1935, it was argued that the Supreme Court should not have jurisdiction over this case as it involves a dispute between two states about their territorial boundaries. The dissenting justices believed that such disputes should be resolved through negotiation and agreement between the states involved rather than by judicial decision. They also expressed concern about setting a precedent where federal courts could intervene in state boundary disputes which they saw as potentially undermining state sovereignty. Furthermore, they disagreed with the majority's interpretation of historical documents and treaties used to determine the boundary line, arguing instead for an alternative reading of these sources which would favor Wisconsin's claim to disputed territory on Lake Michigan.