Griswold served as judge of the Supreme Court of Connecticut from 1807 to 1809. He was presidential elector on the Charles Cotesworth Pinckney and Rufus King ticket. He was the Lieutenant Governor of Connecticut from 1809 to 1811, and was the Governor of Connecticut from 1811 until his death in Norwich on October 25, 1812. He is interred in Griswold Cemetery at Black Hall, in the town of Lyme (now Old Lyme, Connecticut). When Griswold, Connecticut was incorporated in 1815, it was named in his honor.