The answer is "yes". Since the HSA distributions do not enjoy tax-exempt status in New Jersey and since the HSA distributions are, by definition, not reimbursed by insurance, they qualify to be deducted in New Jersey.

However, you do not need to enter them, because TurboTax will handle them automatically.

In the New Jersey interview, on the screen entitled "Any Medical Expenses?", you will see the reference in the text to your HSA.

Click "yes" and the next screen will be "Medical Expenses". You should see your HSA distributions appear on the first line. If that number is correct, just continue to complete your return.