If you have not checked your TurboTax account please do so first, this is just to make sure you E-Filed and it was accepted. If you have already checked, and TurboTax confirmed that YES it was E-Filed, then you will have to contact the state again. Once the return is sent off through TurboTax we only receive updates about the status of the return.
https://www.tax.ny.gov/pit/file/refund.htm
