From The Advocate:
The Attorney General of South Dakota has taken the position that “country clerks in his state who oppose marriage equality on religious grounds can refuse to issue marriage licenses to same-sex couples, so long as another clerk in the office will issue the license.” And if every clerk in the county refuses to issue licenses, “the state itself could issue the license.”
In other words, the South Dakota Attorney General is suggesting that the county clerks' official duties should be defined by their religious beliefs. This may not be the soundest legal advice he's ever offered.