Most states tax you on
So for 2019 I think so. See https://incometax.utah.gov/instructions/who-must-file to determine the answer for self. Typically you will, in the TT interview, allocate every item of income and every deduction so that Utah taxes only the portion of your income earned through your moving date in May. Also check the filing requirements in UT to make sure you have to file.
For 2020, pay attention to the domicile rules
Still owning property is one of the things that can indicate you are domiciled there. But it is a squishy test.
Even if you aren't domiciled if you rent that property the income will certainly be taxed by Utah as would any gain upon sale (both are from UT source income). Even you don't own the property but have a place to stay the issue will be are you domiciled.