Some folks argue that the 10th Amendment would allow it: "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."
But of course no federal bureaucrat or judge would agree.
So the only way to do it democratically would be by a new amendment to the Constitution, one that would allow citizens of a state to vote on the issue.
Good luck getting that one passed.
And it all goes back to this. The US government is strongly for letting folks everywhere else in the world vote on independence. But it ain't happening here. That's ironic, to the point of being hypocritical.
To be fair, the US government didn’t seem happy about the prospect of Scotland seceding. I have been pretty annoyed at some Americans who have watched a lot of Braveheart and ignorantly perceive Scotland as a colony under an English boot advocating the destruction of our union when they would be horrified and bitterly opposed to even allowing a vote on the issue with THEIR country. What is good for the goose is good for the gander and all that.