As Webster 1913 asserts, scot can refer to a payment, charge, or assessment of tax. Therefore, to get off "scot free" means to avoid paying anything. Modern usage has widened the meaning, so that it now suggests escaping punishment (usually unfairly).
I have seen it suggested that the derivation of the word scot may have come from a reference to the tax levied against the English in order to fund hostilities against the Scots.
It is sometimes also suggested that the scot in "scot-free" refers to Dred Scott, an American slave who sued for his freedom and lost, in which case "scot-free" acquires the ironic meaning, "not free at all".
Given the antiquity of the word scot (1), along with the widely used, non-ironic meaning of "scot-free", and the usually-preferred spelling of that expression, I feel that the former explanation is far more likely to be correct.
(1) The Medieval Sourcebook page "Henry I, King of England: Grant of Tax Liberties to London, 1133" at http://www.fordham.edu/halsall/source/1133Hank1tax.html contains the interesting phrase, "let them be quit (i.e. free) of scot".
SEE ALSO : scott free