Yes, you are required to file two Part Year Resident state tax returns.
Income is taxable in the state where the work is performed.
Personal Info section in TurboTax asks
about your state of residence. Since you moved to MO in August, indicate MO as
your residence and that you
lived in another state, you'll be asked to enter a date you became a resident
of a new state. This will ensure that Part-year residency is assigned to you
when filing both state tax returns.
https://ttlc.intuit.com/replies/3302008
