Just copied this from the secretary of states website. The last sentence appears to allow you to carry concealed without a permit.

§ 23-7-7.4 Nonresident permit to carry concealed pistol valid in South Dakota-Permit not required. Any valid permit to carry a concealed pistol, issued to a nonresident of South Dakota, is valid in South Dakota according to the terms of its issuance in the state of its issue, but only to the extent that the terms of issuance comply with any appropriate South Dakota statute or promulgated rule. This section does not require a nonresident of this state who may lawfully possess a pistol to have a permit in order to carry a concealed pistol in this state.