Once your return is accepted for processing by the IRS and/or State TurboTax has no control over the processing of your return and/or release of your refund. If you have any inquiries regarding any delay, you should contact the IRS or your state Department of revenue directly for further assistance.
You should contact NY Department of Revenue for additional information. See link below
https://www.tax.ny.gov/pit/file/refund.htm