1. Because she intends to move back to Connecticut and not make North Carolina her home (at least for now) she would file as a nonresident for North Carolina.
2. North Carolina allows you to file a separate state return if you are a nonresident with no North Carolina income. However, to do so, you have to create a MFS federal return (NOT FILED) using her information and income only to file the North Carolina separate return (and you must mail the faux return with your North Carolina return, see How do I prepare a joint federal return and separate state ).
Because you are both nonresident, if you filed North Carolina as a joint return, your income would not be taxed, but North Carolina uses the total income to determine the tax rate applied to the income so your may pay more tax using this method.
The process itself is simple if you go step by step.
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