Not all states have the same rules.
You are most likely a resident of Minnesota for tax purposes. See below.
Nonresidents If you were a resident of another state but lived in Minnesota, file a Minnesota income tax return as a Minnesota resident if both of these conditions applied to you:
• You were in Minnesota for 183 days or more during the tax year
• You or your spouse owned, rented, lived in, or leased an abode (house, townhouse, condominium, apartment, mobile home, or cabin, with cooking and bathing facilities in Minnesota, that could be lived in year-round)
If both conditions apply, you are considered a Minnesota resident for the length of time you maintained an abode in Minnesota.
See page 5-6:
http://www.revenue.state.mn.us/Forms_and_Instructions/m1_inst_16.pdf
Either way, you'd have a Minnesota return if you worked there. But you are likely considered a resident. Because South Dakota doesn't have a tax, there's no conflict there.
