Answer No. The purpose of that question is to see if you need to file a state tax return for another state.
Having earned money in another state does not reduce the amount of tax calculated for your home state.
This is the general rule: The income is work state (WS) source income since it was earned there. Resident States (RS) tax all their resident's income, regardless of where earned. You will file a non-resident tax return for the WS and report the WS income. You will file a full year resident return for the RS, reporting all your income. The RS will give you a credit, or partial credit for any tax paid to the WS. Since your WS (TX) doesn't have a tax, all that is moot.
