If we lived in Idaho for at least eight months plus do we still have to apply for a non-resident of Utah or do we have to do both

[KrisD · Accepted solution]

If you lived in two states, and have income for both, you would be "part-year residents" for both states and file as such. 

[demeraewright]

We only got income in Utah but we moved to Utah at the end of September

[KrisD]

If you only have income for Utah, you would file as "part-year" resident of Utah. If you earned NO income while living or working in Idaho, including prize or gambling winnings, there is no reason to file an Idaho return (unless you paid tax there that you could get refunded, but that sounds unlikely in your situation)