After the issuance of bonds is authorized as provided in § 6-3-10, it shall be lawful for the county and municipality to join in the erection and completion of such building, and they shall have authority to make provisions for the maintenance of the same. The site for any such building shall be determined upon by the commissioners and the governing body and they shall have authority to use any site owned by either or they may secure a new site.
SDCL 6-3-12