I lived in cali until the end of march last year, worked two weeks and couldn't get another job so I moved back around September... so:
1. Do I file taxes for utah?
2. Do I file taxes for partial/non residence for either cali or utah?
I worked 2.5 months + 2 months in cali.
Yes, No matter what your circumstances it is always better to file a tax return even if you feel that you are exempt from this requirement. As to which state you file a tax return with, normally, you file one with the State in which you had income and one with the State in which you live.
How long you worked is 100% irrelevant. If Charlie Sheen only works 1 week on Two and a Half Men and makes $2 million....does that mean that he should not have to pay taxes on that? See how quickly time becomes irrelevant??