Buying house in S. Carolina

I am a Canadian resident with American citizenship. If I buy a house in S.C. at a price much lower than the current assessment, is the property tax I pay based on the sale price, or the current assessment?

always current assessment.

Bear in mind as a Canadian resident you are subject to Canadian taxes, including capital gains taxes on your second property. Given the state of the real estate market in the US though I doubt that's a big deal (but it might be in the future).

The assessment in a lot of jurisdictions is based on the sale price, you buy it for $100,000, the assessment value for that year becomes $100,000. This is one of the reasons so many States are having financial difficulties.