Yes, you can file up to 5 states in TurboTax Online. If you are paper filing the other state, however, you will not be able to attach the other state return to your e-filed Minnesota return.
That may be different if the other state was Michigan or North Dakota in your case: What is a state reciprocal agreement?
To change from paper filing to e-filing:
For TurboTax Online: How do I change from mail to e-file in TurboTax Online
For TurboTax CD/Download: How do I change from mail to e-file in the TurboTax CD/Download
Otherwise, for filing a paper return, see:
How do I print and mail my return in TurboTax Online?
How do I print and mail a return in the TurboTax for Windows CD/Download software?
How do I paper-file in the TurboTax for Mac CD/Download software?
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