You are considered a part year resident of both states. You need to file a part year resident return for Utah, and as I'm sure you know, you don't need to file a Washington return since they don't have an income tax. As for the 1099, it depends upon what kind of 1099 and what you received it for. It could be a prize, not subject to self-employment tax, or it could be for work as an independent contractor which would be self employment income.
If the 1099 was not for work, then enter as "Other Income" in the wages and income section.
