I lived and worked in Missouri for a large national corporation (has offices in multiple states). I have recently moved to Colorado and changed my residency to Colorado, but am working the same job in Missouri (just telecommuting from CO home instead). I occasionally go back and work in the office in Missouri, but am telecommuting 80% of the time from my home in Colorado. How does income get assigned to the two states.
Your employer should keep up the tally and report it on your W-2 at the end of the year ... talk to them.
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.