State tax filing

The way this works is this:

1. If the HSA contributions are made through your employer, they appear in box 12 of your W-2 with a code of W. This amount is removed from Wages in boxes 1,3, and 5 before your W-2 is printed. 

2. Therefore, since federal income does not include the HSA contributions made through the employer, these contributions must be added back to CA state income (which is derived from federal adjusted gross income).

3. On the federal return, the excess HSA contributions are added to Other Income, because these contributions that turned out to be excess were removed from Wages before the W-2 was printed. 

4. As for as CA is concerned, there is no such thing as an excess HSA contribution, so the excess HSA contributions found in the federal Other Income has to be removed from CA state income.

5. Simply put, whatever was done on the federal return vis-à-vis the HSA needs to be undone in CA. TurboTax does this automatically, on the assumption that your return is 100% CA. This include any penalties paid if you had rolled over the excess contributions, and any penalties for taking a distribution for non-medical expenses.

6. You use the word "refund" - do you mean the amount of excess contributions withdrawn from the HSA? CA does not care if you withdrew the excess or not, CA only cares if the excess was added to Other Income. If this is puzzling, just think of an ordinary investment account on your federal return. What would CA think of you making contributions to that account (hint: nothing)? What would CA think about you withdrawing amounts from the account (again: nothing)?

As for double taxation, most states make some effort to avoid it in a variety of ways. HSA things in Arizona are taxed just as they are (or aren't) on the federal return, while CA undoes everything the federal return does. I don't see anywhere where the question of double taxation would apply.

Does that cover everything?