You can track it at the New York State Department of Taxation and Finance Check Refund Status page.
The state will ask you to enter the exact amount of your expected refund in whole dollars. You can find this by logging into TurboTax. If you're using the mobile app, you may need to scroll down to find your refund amount.
You do not need an Online Services account to use the Check Refund Status page.
You can sign up for email alerts to find out when your return has been processed and also see the date your refund is scheduled to issued.
The refund date you'll see does not include the days your financial institution may take to process a direct deposit or a paper check may take in the mail. If you're concerned, contact the New York State Department of Taxation and Finance.
As much as we would like to help, TurboTax does not distribute refunds, only the IRS or your state tax agency can legally do so.