You have to pay Utah tax on the income you earn for working in Utah. Since you live in Michigan, all your income is subject Michigan tax, no matter where the income is from. But you will get a credit on your Michigan tax return for part or all of the tax that you pay to Utah. You have to file two state tax returns, a Utah nonresident tax return and a Michigan resident tax return. After preparing your federal tax return, prepare your Utah nonresident tax return first, then your Michigan resident tax return, to make sure that the credit is calculated correctly.
You will have to file a Utah nonresident tax return, and pay Utah tax, no matter how little you earn in Utah or how little time you spend there. Utah requires you to file a nonresident tax return if you have any income from Utah at all and you are required to file a federal tax return.
