First, you need to be sure your state return was successfully filed. If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the Tax Home in your Online account.
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
The FAQ below tells how to check on a state refund and has a link for your state. Then you'll see information for your state (which may include info on how long it takes in your state) and a link to go to your state's "Where's My Refund" tool. Your state may also have a FAQ section at it's "Where's My Refund" site that tells how long to expect in your state.
Choose your state from the table in this FAQ. It will also provide you info on contacting the MN Dept. of Revenue should you need additional info.
FAQ: How do I track my state refund?
Once your return is accepted for processing by the IRS and/or State TurboTax has no control over the processing of your return and/or release of your refund. If you have any inquiries regarding any delay you should contact the IRS or your state Department of revenue directly for further assistance.
There is a couple of FAQs to help you track your refund
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?
Why do some refunds take longer than others?
What if my IRS refund is taking longer than 21 days?