Possibly.
(Note that Turbotax can only calculate this for state income tax refunds. Any other kind of refund you have to figure out yourself.)
To see if provider refunds are taxable, you must consider the tax benefit rule. That is, did you previously get a tax benefit from the expense that is now being refunded? Let me give some examples.
1. You paid for the medical expense out of pocket, and did not take the medical expense itemized deduction. You got no benefit from the expense, so if the provider gives you a refund, you have no taxable benefit.
2. You paid for a medical expense out of pocket. Your total expenses were $8,000 and your income was $60,000, so the amount of deductible expenses was $3500 ($8000 minus 7.5% of your income which is $4500). Then you get a $1000 refund from the provider. Because you got the full benefit of that $1000 tax deduction, it is taxable now.
3. You paid for a medical expense out of pocket. Your total expenses were $8,000 and your income was $60,000, so the amount of deductible expenses was $3500 ($8000 minus 7.5% of your income which is $4500). Then you get a $4000 refund from the provider. In this case, you only got a $3500 benefit from the deduction, so only $3500 is taxable. (Because, only $3500 of the expense was over the threshold in the first place.)
4. You paid for a medical expense using tax-free money from an HSA. The provider gives you a refund. If you can use the money for current medical expenses, then you have no benefit from the refund, since tax-free money is still going to pay eligible medical expenses. But if you don't have medical expenses and you just keep the money, it is taxable to you because you got a tax savings from the expense--it's basically the same as a refunded deduction.
