Assuming your move was this year, for 2019 you'll file a part-year resident tax return in both MO and CO. MO can tax all the income you earned as a resident of MO; CO can tax all the income you earn as a resident of CO, regardless of where earned. You became a resident of CO on the date you began living in your new home in CO.
As to whether MO can continue taxing your income after your move to CO (in addition to it's being taxed by CO), as of 2018 the only states that were taxing non-resident telecommuters were NY, NJ, PA, DE, and NE. Of course this may or may not change for 2019.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
