Each state has its own laws and tax rates. They also have provisions to help residents avoid double taxation, such as by allowing credits for taxes paid to another state.
If you were a California resident for the first part of the year, you would file a California part-year resident return and a Utah Resident return.
Prepare the part-year resident California return first. Only your income earned in California would be taxed there. Note the tax liability for California (not the withholding or the amount due with the return, but the actual total California tax computed). See here for California's residency rules.
Then, you may be able to take a credit on the Utah return for taxes paid to California - IF there was any duplication. From the date you become a Utah resident, Utah will tax you on all of your earnings including those from another state. See here for Utah's rules.
You can delete the state returns and prepare them again if needed in order to get these results.
See also this TurboTax article and this one on multiple-state situations.
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