S.D. Codified Laws § 14-2-33
When a county is the local governmental unit petitioned under the provision of § 14-2-32 and that county contains within its geographical boundaries one or more municipalities which provide and support public library services, then the petition shall be signed only by those people living outside of, and the election mandated in § 14-2-31 shall be held only outside of, the boundaries of such municipality or municipalities; provided, however, that by a resolution of the governing body of a municipality, such municipality may be included in the election and if a majority of both county and municipal voters, voting separately, vote to provide county library services then such municipal public library services shall cease and henceforth be provided the municipality by the county governmental unit.
SDCL 14-2-33