The Twelfth Amendment to the United States Constitution was a response to the problematic election of 1800, which resulted in a tie between Thomas Jefferson and Aaron Burr, both of whom were from the same political party. This led to a protracted electoral crisis that exposed significant flaws in the previous electoral system outlined in the Constitution. To remedy this situation, Congress proposed the Twelfth Amendment in early 1803, which allowed for separate Electoral College votes for President and Vice President, ensuring that the two offices would be filled independently. The amendment aimed to streamline the electoral process and prevent similar complications in future elections.

New Hampshire, as one of the early states in the Union, played an important role in the ratification process. On June 15, 1804, the state became the tenth to ratify the amendment, bringing it closer to the required two-thirds majority for adoption. The New Hampshire legislature recognized the necessity of a more straightforward and clearer electoral process and voted in favor of the amendment, understanding its implications for the political landscape. By this vote, New Hampshire contributed to shaping the electoral framework that would govern future presidential elections in the United States.

Ultimately, the Twelfth Amendment was ratified by the necessary number of states and became part of the Constitution in September 1804. It established a fundamental change by altering the way the President and Vice President were elected, ensuring clarity and fairness in the electoral process. New Hampshire's timely decision was a key milestone in the evolution of American democracy, reflecting the state's role in addressing challenges faced by the nation as a whole.