Yes, it is possible that you can get a federal refund and have your MN refund be zero. Your question appears to have been cut off so you may need to repost/clarify. Be advised we cannot see your return in this forum.
If you are confident you entered all income form (W2s, 1099s) information, then TurboTax will have automatically transferred all the pertinent information to your state return. There are normally not many, if any, number entries/calculations necessary in the state returns limiting the error possibilities.
You can view your form 1040 and a summary of your state returns. There you can verify all income is accounted for and verify the Fed Adjusted Gross income transferred to your state return.
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"Tax Tools" in the left hand menu
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"Tools"
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"View Tax Summary" in the main screen
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"Preview my 1040" or "MN State Summary" in the left hand menu
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