No. You will want to enter the dates and rates for the states where you actually lived. Keep in mind this is an itemized deduction item. If your total deductions do not exceed the standard deduction for your filing status you will not see a change in your refund or tax owed.
Additionally, if itemizing the state and local taxes paid deduction is limited to $10,000.
You are right to explore this deduction since your home state (TX) does not have a state income tax.
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