I only lived in CA for 3 months last year. I'm told that I would file a partial year return and the state taxes I paid for that time will be returned to me?

It depends. Usually any part year state will look at your income for the year to determine filing requirements. Each state taxes your part year income that was earned during your residency so depending on the amount you may or may not get a refund. 

You will file both the California (CA) as a part year resident and report all income received while you were a resident.  File the second state, if they have an income tax, and also as a part year resident in that state.  The current resident state will tax income earned during your residency in that state.

There is no credit for taxes paid to another state in this situation.  Each state does want the tax that belongs to them on the money you earned during residency.

As of 2022, Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington, and Wyoming are the only states that do not levy a state income tax.

Q. I only lived in CA for 3 months last year. I'm told that I would file a partial year return and the state taxes I paid for that time will be returned to me?

A. No, that's unlikely.  If you only had CA tax withheld, on the wages you earned, while living there, it's more likely that the amount that was withheld is close to the correct amount.

Whether or not, you get a refund, you are still required to file a part year resident return.