Be safe rather than sorry. There is no hospital in Kadoka. There is a small hospital in Phillip in the next county but it is not equipped for serious trauma. For that, you need to go to Rapid City, which is 90 miles away. Even then, Rapid City has only 1 neurosurgery group and it does not have all the sub-specialties that exists.
The water in Kadoka tastes funny. It tastes like minerals. It have a chemical or gasoline taste as does water in a rest stop near Zanesville, Ohio (USA). If you are accustomed to a certain taste of water, consider bring your own bottled water to Kadoka.
It's only open for 2 hours a day so you have to plan ahead. It is worth a visit if you are in Kadoka.