If you are exempt from state taxes, then the information statement (e.g. Forms W-2, 1099-R ) that you receive should not reflect any taxable income.
If your income is military, or law enforcement, or public service, etc. related, the TurboTax program will prompt you to enter the necessary information to show that the income is not subject to state taxes.
Any other income (e.g. unemployment benefits) that is taxable for Federal purposes and not the State, will be entered in the Federal Section of TurboTax, and adjusted in the State section of the return.
You will need to clarify the type of income that is not subject to state taxes.