Here is a little info from my perspective as a former South Dakota homeowner and Realtor now living in Lincoln, NE and looking to buy as well.
In SD most counties assess taxes based on X percent of the appraised value. My house in Vermillion was assessed at approximately 85% of appraised value. So the house I purchased for $70,000 and appraised for $77,000 was assessed at around $65,000. The local tax authority should be able to tell you how they determine assessed values.
Here in NE it is a different story, they seem to assess taxes based on the appraised value or sale price. I am basing this on the assessed values of several co-work's homes and a number of houses I am currently considering for purchase. One particular property that I am very interested in has an assessed value of $192,000, which is the approximate purchase price from 2003. It is currently listed at 159,900 and I "hope" to offer somewhere around $145,000 and file for a tax assessment recalc.
