Some added detail:
If you move this year (2020), for tax year 2020 you'll be filing as a part-year resident in both MT and OR. MT can tax ALL the income you earn as a MT resident. It can also tax the income you earn by physically working in MT after you become an OR resident*. OR can tax ALL the income you earn after you become an OR resident, regardless of where earned. You'll be able to take a credit on your OR return for the MT tax you pay on the portion of your MT income that you earn after your move.
If your employer will not or cannot withhold OR tax, you may want to begin making quarterly estimated tax payments to OR after your move. This reference gives the details on that: https://www.oregon.gov/DOR/forms/FormsPubs/publication-or-estimate_101-026_2019.pdf
*You become an OR resident for tax purposes on the day you begin living in your new home in OR.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
