South Dakota Codified Laws
12-11-5. Special election to fill senate vacancy. The special election to fill the vacancy of a senator shall be held at the same time as the next general election. The general election laws shall apply unless inconsistent with this chapter.
Source: SL 1979, ch 99, § 2.
The US Constitutional difference between replacement of a House member & replacement of a Senator is that a special election must be held in the case of a House member, but is left to the legislature of the state to determine how to replace in the case of a Senator.
Harry Reid announced that he is now in favor of life support.... at least for two years.....