You would track it on your state's website; not the IRS's. Only federal is tracked through IRS's site. Only your state's website can give you the most up to date status since they are the ones processing your returns and approving your refunds. Once they accept your return, they no longer provide any updates to TurboTax. Processing times vary from state to state. Patience is virtue.
If you are checking and it shows processing on their end, they are working on it. If you check and it says no record and you show as accepted in TurboTax, that just means they have not started reviewing/processing it. Once they start review/process stage, then they update their website with a status.
How do I track my New York tax refund?
