It became rather fashionable starting around the 1920s to ascribe the Civil War to the question of protective tariffs. Partly this was because Marxian analysis (as opposed to Karl Marx himself) engaged in a reductionistic understanding of all of human history to economic interests. Ending slavery, especially with the moral tone the abolitionists used, could not possibly be the reason; it had to be something more fundamentally economic in nature. (And some libertarian ideologues have therefore started making excuses for why the South was really a proto-libertarian society.)
I have seen a number of secession ordinances around the web that give the threat of ending slavery as the reason for states to secede--but only a few state secession ordinances are usually listed. Here is an 1893 book that lists all of the state secession ordinances. Only some of them list slavery--but the other give no specific reasons. And none of them mention tariffs. This is hardly conclusive proof--but you would think if tariffs were the issue, or even a significant issue that at least one state would have mentioned it.
There was discussion of this once the war was well under way, but this 1863 book argues that since the South had actually been on the side of protective tariffs for some products in 1857, it was certainly not a genuinely pro-free market motivation. At least some contemporary works argue that the tariff claim was manufactured for the purpose of promoting the Confederacy in Europe.