TurboTax does not receive any kind of tax refund, federal or state.
If you had a tax refund from the amended tax return, the IRS would have mailed a refund check to the address on the tax return.
If you never received the mailed check, then go to this website for a missing check - https://www.irs.gov/faqs/irs-procedures/refund-inquiries/refund-inquiries-0