The state of South Dakota recently announced an index to a database of cemetery records. You can now do Cemetery Records Search at http://apps.sd.gov/applications/DT58Cemetery/ . As the site makes clear, this is NOT an index of all burials in South Dakota, but mostly the result of a survey of cemeteries in South Dakota in the 1940s. (The “Graves Registration Project”.)
You can search by first and last name, city and county, and cemetery name. A last name search for Smith found — argh — a lot of results, with no result count, from Fred Bauersmith to James H Smith (I am suspicious this is incomplete.) Result listings include name, death date (occasionally unknown), block and lot number, city and county, and cemetery name. And that’s it. You can request the full cemetery record by going to the archives (of course) or filling out the Cemetery Record Information Request form. Requesting one name is $10.60, but 2 to 5 names will run you $21.20.