Given the reputation of Scotsmen as being careful with their money we might look to Scotland for the origin of 'scot free'. Wrong again.
'Skat' is a Scandinavian word for tax or payment and the word migrated to Britain as early as the 10th century, then mutated into 'scot' as the name of a redistributive taxation. The term is a contraction of 'scot and lot'. Scot was the tax and lot, or allotment, was the share given to the poor.
Scot as a term for tax has been used since then to mean many different types of tax. Whatever the tax, the phrase 'scot free' simply refers to not paying one's taxes..
An example of the current commonly used form, i.e. 'scot free', comes a few years later, in Robert Greene's Pandosto: or, The Historie of Dorastus and Fawnia, 1588:
An early use of the figurative version of the phrase is found John Mapley's Green Forest, 1567:
"Daniell scaped scotchfree by Gods prouidence."
It presently has a wider use of meaning not being punished for something that you have done."These and the like considerations something daunted Pandosto his courage, so that hee was content rather to put up a manifest injurie with peace, then hunt after revenge, dishonor and losse; determining since Egistus had escaped scot-free, that Bellaria should pay for all at an unreasonable price."