Tax calculations

When the IRS or a State sends you a letter indicating you owe taxes on the tax return that was filed but what you filed showed a tax refund, then the issue is that you more than likely did not report some type of income.  The IRS and State receive all types of forms based on your Social Security number so if you failed to report that income the IRS or State will calculate the taxes you owe and if the taxes owed are greater than the taxes you paid then they send you a bill.

The state letter you received should have indicated the income that was added to your tax return and how they calculated the taxes owed.

You have not mentioned what the state changed on your return that resulted in you owing instead of getting a refund.   TurboTax guarantees its calculations---but cannot guarantee that users enter all of their information completely and accurately.  

TurboTax provides do-it-yourself tax software.  TurboTax guarantees the calculations done by its software.   The information entered into that software is data entered by you, the user.   TurboTax cannot and does not check that information against any outside sources, so TT cannot know if you entered your information completely or correctly.   It is up to you to enter all of your information correctly and completely, and to check your tax return before you file it.  If you forget to enter some income, or enter it incorrectly, enter it in the wrong place, etc. then you may end up owing additional tax to the IRS and/or state.  TurboTax does not pay the additional tax you owe.   If TurboTax’s calculations were incorrect, and you owe penalties and/or interest, then TT will pay the penalties and interest.  The tax due is always owed by you, and must be paid by you.

If you need to enter a claim for the accuracy guarantee:

https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-account-billing/submit-claim-turb...