South Carolina did not, the legislature set up the convention and approved secession on their own. North Carolina put the matter to the people, who voted against it, and then the legislature seceded anyway. The Texas legislature and the Virginia legislature voted to secede, claiming that the action was pending the approval of a popular referendum, but both states were admitted to the confederate states before those referendum took place.
But that didn't answer the question, did any of the state legislatures have the authority Rawle mentioned to take their state out of the Union? If so, then what gave them that authority and when did they get it?
The Texas referendum by the voters took place on Feb 23, 1861. The first I see of the Confederate Congress giving any official role other than observers to the TTexas delegation was on Feb 27, 1861, when they were given power to discuss and vote on matters specifically relating to the permanent Constitution which did not pass until sometime later.
The Texas delegates were instructed by the Texas Secession Convention on March 5, 1861, to apply for admission as a state to the Confederacy.
The SC General Assembly, on 10 Nov 1860, called for a convention - comprised of the people of SC. On 17 Dec 1860, the convention convened in the Baptist Church in Columbia SC. From their convention:
We, the People of the State of South Carolina, in Convention assembled, do declare and ordain, and it is hereby declared and ordained,North Carolina put the matter to the people, who voted against it, and then the legislature seceded anyway.That the Ordinance adopted by us in Convention, on the twenty-third day of May, in the year of our Lord one thousand seven hundred and eighty-eight, whereby the Constitution of the United States of America was ratified, and also all Acts and parts of Acts of the General Assembly of this State, ratifying amendments of the said Constitution, are hereby repealed; and that the Union now subsisting between South Carolina and other States, under the name of "The United States of America," is hereby dissolved.
No. In March 1861 the people of the state voted against calling a convention 46,672 to 47,269. After Sumter was attacked the state did call a convention of the people, which on 20 May 1861, passed the following:
We, the people of the State of North Carolina, in Convention assembled, do declare and ordain, and it is hereby declared and ordained, That the ordinance adopted by the State of North Carolina in the Convention of 1789, whereby the Constitution of the United States was ratified and adopted, and also, all acts and parts of acts of the General Assembly, ratifying and adopting amendments to the said Constitution, are hereby repealed, rescinded and abrogated.The Texas legislature and the Virginia legislature voted to secede, claiming that the action was pending the approval of a popular referendum...
When did the people reject that recission? The Confederate States of America admitted Texas as a state on 2 Mar 1861, which the Texas convention accepted on 5 March AFTER secession was approved by the people of the state:
The People of Texas, in Convention assembled, Have ordained and declared, and do hereby ordain and declare, that the delegation aforesaid, to the Congress aforesaid, be, and they are hereby instructed, and we do accordingly instruct them, in behalf of the State, and as representing its sovereign authority, to apply for the admission of this State into said Confederacy; and to that end and for that purpose, to give in the adhesion of Texas to the provisional Constitution of said Confederate States; and which said Constitution, this Convention hereby approves, ratifies and accepts.Regarding Virginia, the legislature called for the election of 152 delegates to a convention which convened in Richmond on 13 Feb 1861. On 17 Apr 1861, these delegates, not the legislature, passed an Ordinance of Secession by a vote of 88 to 55.