That would actually depend upon the wording of the Act which admitted the State to the Union.
As I understand the matter, there is a general assumption in law of the competence of the individual to perform any act, and the right to perform any act which is not specifically forbidden in law.
However, a legal entity, such as a State or corporation, can only act within the parameters of the legal instrument by which it was created. Therefore, unless secession is specifically permitted by either the Constitution of the United States or the individual Constitutions of the States themselves, it is not a legal act.
That's my view as a layman, not a lawyer. (I couldn't grow the necessary dorsal fin.)