It depends if you intend to stay in the new state, @TomD8 is correct. Temporary residences would not necessarily subject you to filing a part-year resident tax return.
In general, it would appear you need to file a part-year return for Illinois only if no income was earned in the other state. However, some states may require taxing income earned while living in their state even if they allow a credit for what was paid to Illinois.
I recommend entering both states in TurboTax, with the state you were living in on December 31, 2020 entered last. If your new resident state does not require any tax, be sure to delete that state before paying for the program.
See: How do I file if I moved to a different state last year?
How do I contact my state Department of Revenue?
