The Resident tax state lets you take a credit for yoru tax liability to the non-resident state (not what was withheld in the non-resident sate...just what the nonresident state actually calculates for the total tax due them...before considering withholding).
Thus, the nonresident state needs to be full done first, so that exact value will be transferred to the Resident tax form. OF course, every scrap of the Federal tax return needs to be filled in first, before either state is worked on.
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And if the two states are reciprocal tax states...the situation changes considerably.