William Williams was a Congregationalist and a devout Christian.
He was identified as a Congregationalist by The Congregationalist Library. (Source: Ian Dorion, "Table of the Religious Affiliations of American Founders", 1997).
From: B. J. Lossing, Signers of the Declaration of Independence, George F. Cooledge & Brother: New York (1848) [reprinted in Lives of the Signers of the Declaration of Independence, WallBuilder Press: Aledo, Texas (1995)], pages 56-58:
Wales was the place of nativity of the ancestors of William Williams. They emigratd to America in 1630, and settled at Roxbury, in Massachusetts. His grandfather and father were both minsters of the gospel, and the latter was for more than half a century pastor of a Congregational Society [a Congregationalist congregation], in Lebanon, Connecticut, where [William Williams] was born on the eighteenth of April, 1731. He entered Harvard College at the age of sixteen years, and at twenty he graduated with honorable distinction. He then commenced theological studies with his father; but the agitations of the French War attracted his attention, and in 1754 he accompanied his relative, Colonel Ephraim Williams, in an expedition to Lake George, during which the Colonel was killed. He returned home with settled feelings of dislike toward the British officers in general, who haughtily regarded the colonists as inferior men, and deserving of but little of their sympathy.
He abandoned the study of theology, and entered into mercantile pursuits in Lebanon. At the age of twenty-five he was chosen town clerk, which office he held nearly half a century. He was soon afterward chosen a member of the Connecticut Assembly, and forty-five years he held a seat there. He was always present at its sessions, except when attending to his duties in the General Congress, to which body he was elected a delegate in 1775. He was an ardent supporter of the proposition for Independence, and cheerfully signed the glorious Declaration when it was adopted.
When, in 1781, Arnold, the traitor, made an attack upon New London, Williams, who held the office of colonel of militia, hearing of the event, mounted his horse and rode twenty-three miles in three hours, but arrived only in time to see the town wrapped in flames.
Mr. Williams was a member of the State Convention of Connecticut, that decided upon the adoption of the present Constitution of the United States, and voted in favor of it. His constituents were opposed tot he measure, but it was not long before they discoverd their error, and applauded his firmness.
In 1804, Colonel Williams declined a re-election to the Connecticut Assembly, and withdrew entirely from public life. His life and fortune were both devoted to his country, and he went into domestic retirmeent with the love and veneration of his countrymen attending him. He was married in 1772, to Mary, the daughter of Governor Trumbull, of Connecticut, and the excellences of his character greatly endeared him to his family. In 1810 he lost his eldest son. This event powerfully shocked his already infirm constitution, and he never recovered from it. His health gradually declined; and a short time bfore his death he was overcome with stupor. Having laid perfectly silent for four days, he suddenly called, with a clear voice, upon his departed son to attend his dying father in the world of spirits, and then expired. He died on the second day of August, 1811, at the patriarchal age of eighty-one years.
From: Robert G. Ferris (editor), Signers of the Declaration: Historic Places Commemorating the Signing of the Declaration of Independence, published by the United States Department of the Interior, National Park Service: Washington, D.C. (revised edition 1975), pages 144-145:
A Congregational pastor's son, Williams was born in 1731 at Lebanon, Conn., his lifelong home. After graduating from Harvard in 1751, he began studying for the ministry under his father. Four years later, during the French and Indian War (1754-63), he accompanied a British expedition to Lake George, in northeastern New York, that won a victory...
Williams died at the age of 80 in 1811. His grave is in the Trumbull Cemetery, about a mile northeast of town.