As far as I know, none of the TurboTax state software for 2022 is available yet. If you are using TurboTax for 2022 and there is something that looks like a state program, it's probably so skeletal and preliminary that it's essentially useless. You can't draw any conclusions from it.
There has to be a residency question in the CT interview. CT has a different form for nonresidents. Maybe you clicked past it too quickly. It would be one of the earliest screens in the CT interview. If you're looking at 2021, go through the CT interview again and read the early screens carefully. Also, in the federal Personal Info section, make sure you said that you have income from other states, and that you selected CT as one of the other states.
As far as CT taxing your non-CT income (if you are looking at 2021, not 2022), probably one of two things is going on. One possibility is that, since you didn't see the CT residency question, you are creating a CT resident return instead of a nonresident return. The resident return would, of course, tax all your income, no matter where it's from. The other possibility is that you are misunderstanding how the CT nonresident tax return works. It first calculates what the CT tax would be on all your income, then prorates the tax based on what percentage of your income is CT income.
When I said "in CT" I meant IN CT.
The W-2 may be a big problem. They can't put zero in box 16, because the state tax withheld in box 17 can't be more than the state wages in box 16. The correct and best solution would be for the employer to refund to you all of the CT tax that they withheld, and not put any state information on the W-2. Just leave boxes 15, 16, and 17 blank. Then you wouldn't even have to file a CT tax return. They can do that. They can get the money back from the state. But they might give you a hard time about it, or say that they can't do it. If they won't do that, then they shouldn't manipulate the W-2 at all. They will have to put the full amount that they paid you in box 16, even though none of it is actually CT income, and the full amount of CT tax withheld in box 17. Then you will have to reallocate the income on your CT nonresident tax return to show that you had zero CT income. If you have to do this, you may need to get help from a tax professional. I'm sorry I can't give you a better answer.
