No.

South Dakota is one of dozens of states that doesn’t require a high school degree or teaching certifications to homeschool children.
South Dakota law places minimal restrictions on teachers who homeschool, also known as alternative instruction. The statute limits them to teaching no more than 22 children and requires that instruction be given "so as to lead to a mastery of the English language."
According to the Coalition for Responsible Home Education, North Dakota is the only regional state to South Dakota that requires a high school diploma or equivalent.
The Home School Legal Defense Association (HSLDA) reports that adults must notify the state's Department of Education within 30 days of starting to homeschool a child.
South Dakota’s rate of homeschooled students increased 143% from 2015-16 to 2023-24, according to a database compiled by Johns Hopkins University, the highest increase of any state that reported data.
This fact brief responds to claims such as this one.
Sources:
HSLDA, How to comply with South Dakota’s homeschool law
South Dakota Codified Laws, 13-27-3 Alternative instruction - Notification – Requirements
Coalition for Responsible Home Education, South Dakota
South Dakota News Watch, Has South Dakota seen the largest homeschool growth of any state?
