You can have your home completely exempted from South Dakota property tax if you lost, or lost the use of, both lower extremities. The exemption covers the house, the garage and up to one acre of the lot they sit on, and an unremarried surviving spouse keeps it.
Apply through your local county director of equalization, not the state. Applications open each January and must be submitted on or before November 1 every year.
The completed South Dakota Application for Paraplegic Veteran Property Tax Exemptions, your VA documentation of the loss or loss of use of both lower extremities, proof that you own the property, and evidence that the home is specifically designed for wheelchair use.