The Oregon rules for whether a dependent is required to file are essentially the same as the federal rules. As far as I can see from the instructions for Oregon Form OR-40, if her only income for the year is $4,300 of wages on a W-2, she should not owe any Oregon tax, and would not have to file an Oregon tax return. So I don't understand how she can owe any tax to Oregon. If she does owe $88, she certainly has to file. But you have to figure out where that $88 is coming from. It's hard to do that here in the Community, because we can't see the tax return.
By the way, you are using the term "tax liability" differently from the way the IRS and tax professionals usually use it. Tax liability is not the amount you owe on your tax return. It's the total amount of tax that you have to pay for the year, whether it's paid by withholding or by a payment when you file your return, or a combination of the two. The amount you owe on your tax return is a payment due or a balance due. You have a tax liability even if you are getting a refund. Tax liability does not depend on how much tax was withheld from your pay.
