Yes, but you can claim a credit on your Utah tax return for taxes you paid to another state. 

According to the Utah State Tax Commission website, "If you are a Utah resident and earned income in another state, you must pay Utah taxes on that income as well as your Utah income. You are still considered a Utah resident even if you work in another state, and must file a Utah income tax return reporting all income, regardless of source. See Residency and Domicile.

Utah residents that have paid taxes on income earned in another state may claim a credit for taxes paid to the other state if the state where the income was earned also taxes the income. For more information, see Credit for Taxes Paid to Another State. Utah residents earning income in a state without an income tax must pay tax to Utah on that income with no credit allowed because no tax is paid to the other state."