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You do not need to have an HDHP in order to take a distribution from an already existing HSA account. You have to have an HDHP in order to contribute to an HSA account.
Contributions usually come from your W-2. When you enter a code W from Box 12, you will need to indicate that you have a high deductible health plan so you are not taxed on the contributions.
To do this in TurboTax, sign in and click on Take me to my return. Then type in hsa into the search field, hit enter, and click on the Jump to hsa link, see attached. Proceed through the questions. You can enter you HDHP info and your distributions, if any, in this interview.
Distributions come from a 1099-SA. You can enter this form in the same area. In order not to be taxed for distributions, you only need to indicate that you used the money for qualified expenses. You do not need to be enrolled in a high deductible health plan in order to use (take a distribution) your HSA funds, only to contribute to an HSA.