Each of those states will require ae a tax return.  You will file as a resident for Missouri and a non-resident for Kansas. Missouri will give you a credit for the tax you pay in Kansas, but only up to the amount of Missouri tax on the same income.  So if you earned 50,000, and Kansas taxes you 2000 but Missouri only taxes you 1800, you will receive a credit of 1800 on your Missouri taxes to bring it down to zero.  You will not be reimbursed further.  And if Missouri has a higher tax rate than Kansas, you will have a balance you still owe to Missouri.

To avoid the double-taxation (or at least the need to fill out two state returns), unfortunate about the only two real options are to either move to Kansas (working and living in Kansas) or work in Missouri (living and working in Missouri). 

Having said that, TurboTax will make sure you are not over-taxed.  In the Personal Info Tab, make sure you answer “yes” to the question if you worked in another state besides Missouri and select Kansas.  Fill out your Kansas return first and TurboTax will transfer all of the necessary information to your Missouri return to calculate and apply the credit.

I only worked 6 months in 2020 in the state of KS - how to I breakdown 1/1/20-3/31/20, 1/1/20-5/31/20 and 1/1/20-8/31/20? I did not live in the state of KS in 2020.

Your resident state taxes all income but gives a credit for income taxed by another state.  Please carefully follow these directions.

You will need to prepare the states in a special order. You may need to delete both states and begin again.

1. First, prepare your non-resident KS return. This creates your tax liability for the non-resident state. How do I file a nonresident state return?
2. THEN prepare your resident state MO return and it will generate a credit for your income already being taxed in the non-resident state.
3. The credit will be the lower of the state tax liabilities on the same income. You may owe your resident state.

It isn't possible for the program to create a credit before it knows the liability. Your returns may be wrong if you do not prepare the states in this order.