You're talking about Winston County AL, and that’s a popular legend. Much has been written about it since the war.

Bottom line: counties have no legislative bodies. They exist under complete authority of the state legislature and cannot secede from a state or join another one. On the other hand, a state can divide a county, rename it or dissolve it. A state can create new counties out of old ones.

Even if counties could secede from a state, it makes no sense to secede and then continue to send representatives to the state legislature, as citizens of Winston did.