Nonresident return
The return you file with a state where you earned income but did not live, reporting only the income sourced to that state.
A nonresident return covers a slice rather than a year. It reports what the state is entitled to tax — normally wages for work physically performed inside its borders — and prorates deductions and credits to that slice, so the state taxes its share at roughly the rate that share would have attracted had it been your only income.
It is filed before the resident return, because the tax it produces is the figure the resident return's credit is based on. Filing them the other way round means doing one of them twice.
Most states set no de minimis for nonresidents: any state-source income above the general filing threshold triggers a return. A few publish a genuine safe harbour — Maine's twelve-day and dollar test is the clearest example — and a few more relieve the employer of withholding below a day count without relieving the employee of filing. Those two things are frequently confused.
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In one sentence
What is nonresident return?
The return you file with a state where you earned income but did not live, reporting only the income sourced to that state.