No. You would only be liable for MN tax, for any days you physically worked in MN.
It's the same in most states. But, New York, Pennsylvania, Nebraska, Delaware and Arkansas have a "convenience of the employer" rule. If you work from home, for your own convenience, you are liable for tax to those states. CT imposes CT tax on some out-of-state remote workers. But it only applies if you live in a state that has the same rule.
