After establishing the origin of the nation, (Chief Justice) Chase next addressed Texas' relationship to that Union. He rejected the notion that Texas had merely created a compact with the other states, but had in fact incorporated itself into an already existing indissoluble political body.[18] From the decision:
When, therefore, Texas became one of the United States, she entered into an indissoluble relation. All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.
For these reasons, Texas had never been outside the Union and any state actions taken to declare secession or implement the Ordinance of Secession were null and void. The rights of the state itself, as well as the rights of Texans as citizens of the United States remained unimpaired. From the decision:
Considered therefore as transactions under the Constitution, the ordinance of secession, adopted by the convention and ratified by a majority of the citizens of Texas, and all the acts of her legislature intended to give effect to that ordinance, were absolutely null. They were utterly without operation in law. The obligations of the State, as a member of the Union, and of every citizen of the State, as a citizen of the United States, remained perfect and unimpaired. It certainly follows that the State did not cease to be a State, nor her citizens to be citizens of the Union. If this were otherwise, the State must have become foreign, and her citizens foreigners. The war must have ceased to be a war for the suppression of rebellion, and must have become a war for conquest and subjugation.
http://en.wikipedia.org/wiki/Texas_v._White