You can read the statutes 13-27 on homeschooling law at: http://www.state.sd.us/state/legis/lrc/statutes/lrcmenu.htm
13-27-3. Child excused if provided alternative instruction -- Application -- Investigation -- Revocation -- Restrictions -- Testing. A child shall be excused from school attendance, pursuant to § 13-27-2, because the child is otherwise provided with alternative instruction for an equivalent period of time, as in the public schools, in the basic skills of language arts and mathematics. The parent or guardian of the child shall identify in the application the place where the child will be instructed and any individual who will instruct the child. The individuals are not required to be certified.
The secretary of the Department of Education and Cultural Affairs may investigate and determine whether the instruction is being provided. Failure to provide instruction is grounds for the school board, upon thirty days notice, to revoke the excuse from school attendance. The secretary of the Department of Education and Cultural Affairs may inspect the records of an alternative education program with fourteen days written notice if the secretary has probable cause to believe the program is not in compliance with this section. The records to be inspected are limited to attendance and evidence showing academic progress.
No individual may instruct more than twenty-two children. All instructions shall be given so as to lead to a mastery of the English language. Children receiving alternative instruction who are in grades tested under the state testing program shall take a nationally standardized achievement test of the basic skills. The test may be the test provided by the state and used in the public school district where the child is instructed or another nationally standarized achievement test chosen by and provided at the expense of the child's parent, guardian, or school giving alternative instruction. The test may be monitored by the local school district where the child is instructed.
Note: This information provided for information only, not as legal counsel