Nicholas Gilman was also a U.S. Representative in the First U.S. Federal Congress (1789-1791).
Nicholas Gilman was a Congregationalist.
He was identified as a Congregationalist by: the Library of Congress and A Worthy Company: Brief Lives of the Framers of the United States Constitution, written by M. E. Bradford. (Source: Ian Dorion, "Table of the Religious Affiliations of American Founders", 1997).
From: Robert G. Ferris (editor), Signers of the Constitution: Historic Places Commemorating the Signing of the Constitution, published by the United States Department of the Interior, National Park Service: Washington, D.C. (revised edition 1976), pages 169-170:
Gilman's career ranged from clerking in a store to long tours of duty in the U.S. House of Representatives... He was one of the three bachelor signers [of the U.S. Constitution]... In...  as a Democratic-Republican he won election to the U.S. Senate. He was still sitting there when he passed away at Philadelphia, while on his way home from the Nation's Capital, in 1814, at the age of 58. He is interred at the Winter Street Cemetery at Exeter.
Note that numerous sources and authoritative references have been consulted in order to ascertain the religious affiliation of the American Founding Fathers. Note that the excerpts and references mentioned on this page are not the only references used in order to identify this person's religious affiliation.