While the constitution does not expressly state against sodomy, thomas jefferson the author of it tried to pass a law:
Three years later, Jefferson drafted a bill concerning Virginia’s criminal law providing that the penalty for sodomy should be castration. See Thomas Jefferson, The Writings of Thomas Jefferson, Andrew A. Lipscomb, ed. (Washington, Thomas Jefferson Memorial Association, 1904) Vol. I, pp.226-27, from Jefferson’s “For Proportioning Crimes and Punishments.”
The bill read: “Whosoever shall be guilty of rape, polygamy, or sodomy with a man or woman, shall be punished; if a man, by castration, a woman, by boring through the cartilage of her nose a hole of one half inch in diameter at the least.” (Virginia Bill number 64; authored by Jefferson; 18 June 1779)(Emphasis added.)
When the Constitution was ratified, a majority of the states (New York, North Carolina, South Carolina, Connecticut, Virginia, Rhode Island, Massachusetts and New Jersey) provided the death penalty for those who committed sodomy. All states prohibited it. [Except Georgia -Bob]
The Constitution Does Not Permit Polygamy or Same-Sex Marriage
and up until about 1962 sodomy was a felony in most states....boy how times have changed ..for the worse....