I work in South Dakota and I live in South Dakota but the company I work for is based in North Dakota. Should I have to pay state income tax to North Dakota?

No.  Your state tax obligations are based on where you actually live and work, not on the location of your employer's home office.  If you did not live in or physically work in ND during the tax year, your income is not taxable by ND.

Thank you TomD8