Article I of the Paris Peace Treaty Reads:
His Brittanic Majesty acknowledges the said United States, viz., New Hampshire, Massachusetts Bay, Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Maryland, Virginia, North Carolina, South Carolina and Georgia, to be free sovereign and independent states, that he treats with them as such, and for himself, his heirs, and successors, relinquishes all claims to the government, propriety, and territorial rights of the same and every part thereof. (emphasis added)
It having pleased the Divine Providence to dispose the hearts of the most serene and most potent Prince George the Third, by the grace of God, king of Great Britain, France, and Ireland, defender of the faith, duke of Brunswick and Lunebourg, arch- treasurer and prince elector of the Holy Roman Empire etc., and of the United States of America, to forget all past misunderstandings and differences that have unhappily interrupted the good correspondence and friendship which they mutually wish to restore, and to establish such a beneficial and satisfactory intercourse , between the two countries upon the ground of reciprocal advantages and mutual convenience as may promote and secure to both perpetual peace and harmony; and having for this desirable end already laid the foundation of peace and reconciliation by the Provisional Articles signed at Paris on the 30th of November 1782, by the commissioners empowered on each part, which articles were agreed to be inserted in and constitute the Treaty of Peace proposed to be concluded between the Crown of Great Britain and the said United States, but which treaty was not to be concluded until terms of peace should be agreed upon between Great Britain and France and his Britannic Majesty should be ready to conclude such treaty accordingly; and the treaty between Great Britain and France having since been concluded, his Britannic Majesty and the United States of America, in order to carry into full effect the Provisional Articles above mentioned, according to the tenor thereof, have constituted and appointed, that is to say his Britannic Majesty on his part, David Hartley, Esqr., member of the Parliament of Great Britain, and the said United States on their part, John Adams, Esqr., late a commissioner of the United States of America at the court of Versailles, late delegate in Congress from the state of Massachusetts, and chief justice of the said state, and minister plenipotentiary of the said United States to their high mightinesses the States General of the United Netherlands; Benjamin Franklin, Esqr., late delegate in Congress from the state of Pennsylvania, president of the convention of the said state, and minister plenipotentiary from the United States of America at the court of Versailles; John Jay, Esqr., late president of Congress and chief justice of the state of New York, and minister plenipotentiary from the said United States at the court of Madrid; to be plenipotentiaries for the concluding and signing the present definitive treaty; who after having reciprocally communicated their respective full powers have agreed upon and confirmed the following articles.
Correct me if I'm wrong but it looks like the treaty was with the United States of America. and not with the individual states.