You can only have one state at a time that is considered your resident state, even though you may spend time in more than one state.
Your resident state is not determined by where you intend for your home to be. It is normally the state where you spend the most time, or the state that you would plan to return to after temporary absences. States also look at things such as where your car and drivers license are registered, where you are registered to vote, where your bank accounts or located, if you own property in a state, where you have local club or church affiliations, and things of that nature.
But since TX has no state income tax, and your income is from NC, then in your particular case your tax situation will really be no different, as you will pay taxes to NC regardless of whether or not TX is where you consider your resident state to be.
The only difference will be in which form you will file. If you consider yourself to be a resident of TX, then you will file a nonresident return with NC and report your income from that state. If you consider yourself a resident of NC, then you will simply file a resident return with NC. Either way in your particular situation you will just end up filing with the state of NC since that is where your income is from.
If you also have income from other states other than NC, you would also need to file nonresident returns with those states and report the income that you earn from each state.
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Thank you cheryl