What article of the Constitution of the United States give a state a method of leaving the United States. Arguably Amendments 9 & 10
- Amd 9 — The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
- Amd 10 — The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
#9 says that any enumeration is non-exhaustive and merely not-being listed is not grounds for denial of it. (A good example is travel at will; not enumerated but essential to a life of liberty.)
#10 Says that the powers not [explicitly] delegated to the federal government remain the purview of the States (or the people themselves).
As there is nothing in the Constitution denying to the states the power to leave they must still retain it. (Such prohibitions are explicitly laid out: prohibition of ex post facto law, prohibition of entering into treaty/alliance/confederation, prohibition against bills of attainder, etc.)