True. Although he resigned his commission in the U.S. Military before he assumed a commission in the Confederate Army. The Constitution does not specify whether or under what procedures a state can voluntarily leave the Union.
It had no need to do so. The procedures were outlined in the earlier founding document known as the "Declaration of Independence."
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
Beyond that, both New York and Virginia had made it clear in their ratification statement regarding the US Constitution that they had a right to reassume the powers they were giving up to the Union. There were no objections to their assertion of this right in their ratification statement.