Richard graduated in 1751 from Yale and read law with Jared Ingersoll.
Richard was admitted to the bar in 1755, and moved two years later to New London. Here he attended the First Church (Congregational). He seems to have been a thorough student of jurisprudence, a master of argument, if not of the art of persuasion, and a highly successful lawyer. His public career commenced in 1765 with his appointment as justice of the peace and with his election to the General Court. He was clerk of the latter during his last two years of membership and until his appointment as assistant, a position he held from 1776 to 1786.
A faithful patriot, he joined in the protest against the Townshend duties and later against the Boston Port Bill, was a member of the Connecticut Council of Safety of 1776, and was one of the two delegates sent to New York to confer with Washington on the defense of the colony (1776). He was chosen a delegate to the Continental Congress in 1774, 1776, 1777, and from 1780 to 1783, but the state of his health seems to have prevented his attendance in 1774 and 1776, for he served only in the sessions of 1777, 1781, and 1782, and then without distinction.
More distinguished was his judicial career in Connecticut. In 1773 he became chief judge of the New London county court, a position that he held until 1784 when he was elevated to the bench of the superior court of which two years later he was made chief judge. In 1789 he was appointed by Washington United States district judge. Early in the Revolution the Council of Safety had requested him to compile a code of maritime law. In 1783-84 he, with the assistance of Roger Sherman, also a superior court judge, codified the statute law of the state, published as Acts and Laws of the State of Connecticut, in America (1784).
In 1784 the freemen of New London unanimously elected Law the first mayor of the newly chartered city. This position, with his federal judgeship, he held until his death. Law was generally Federalist in politics. At the Connecticut Convention of 1788 at Hartford, which so quickly ratified the federal Constitution, he spoke in favor of that document. A year later he was a member of the first electoral college from Connecticut. Yet in the spring elections of 1801 the Republicans named him their candidate for governor. Law declined the nomination, urging his age and disinclination for the office, but no other Republican nomination was made. Consequently he received only 1, 056 votes to 11, 156 for Governor Trumbull, and ran behind his own ticket. Five years later he died at his home in New London.
On September 21, 1760, Richard Law married Ann, the daughter of Capt. John Prentise.