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.
