First, a 401k is not an IRA. Although they are similar, they are controlled by different sections of the tax law. It sounds like you had a 401k with a pre-tax account and a designated Roth account, but you closed them both.
Second, I don't know where in the program you are asked if you "own" a Roth IRA or traditional IRA. It sounds like you don't now, and did not before. You will be asked "did you contribute", but that is not the same as owning. And, unless you left out parts of the story, you never contributed to any kind of IRA, because you contributed to a workplace 401k plan. Those contributions are automatically recorded on your W-2, and you never enter them a second time in the IRA section because a 401k is not an IRA.
Third, you had the option of doing a tax-free rollover from the pre-tax 401k to a traditional IRA at another bank or broker, and rollover the Roth 401k to a Roth IRA. You have 60 days to do this from when you got the check, so if this was less than 60 days ago, you should ask more about that because you can save on taxes and penalties and get the money back into a tax-free retirement account.
If it is more than 60 days, and you cashed out the accounts, then you owe income tax and a penalty for early withdrawal unless you were age 55 or older when you left the company. You will get two 1099-R forms from the 401k custodian in January -- they are supposed to be mailed by January 31, and you may be able to download it from your online account as well. Enter these 1099s into Turbotax. For the pre-tax 401k, the entire amount is subject to regular income tax plus a 10% penalty for early withdrawal. For the Roth 401k, the contributions you get back are tax-free, but the earnings are subject to income tax plus a 10% penalty.
