I moved to Idaho last year. I've not worked since I moved here. State income tax says I have an over payment of $399. I lived in Utah before here

Likely there is income not properly allocated (see below).  However, since you are a part-year resident of ID with no ID source income you do not need to file in ID. Here is the ID reference.  If you did not earn any income while living in ID or from ID sources while living outside of ID, then simply do not file the ID part-year return. When you get to the filing steps; select federal and UT only.  

If you want you can "Continue/Edit" your ID state interview and in the "Income" section you will have the opportunity to allocate income for each of your income sources into or out of ID.  You would allocate zero (0) income to ID.  You would not have an ID filing requirement in that circumstance.