If your state refund was less than what you expected, it may have been offset to pay an outstanding debt in the state of NY or the state made adjustments while processing your return. The state should send you a notice explaining what happened. And if you have questions after receiving that notice, you can contact them at the phone number provided in the letter. TurboTax has no access to what happens after the government receives your returns. They handle all the processing of the returns and refunds after you file.
You may be able to get some information while waiting on the notice, but you'll have to contact NY's Department of Taxation and Finance to see what they can tell you. Here is their contact page https://www.tax.ny.gov/help/contact/default.htm
"Adjusted refund amounts
Your refund amount may differ from what you claimed on your return if:
- your tax return had one or more errors
- If we sent you a paper check, we will also send you Form DTF-160, Account Adjustment Notice. For an explanation of the error(s) on your tax return, see Section A, Explanation of adjustment.
- If we directly deposited your refund, within 30 days we will send you Form DTF-160, Account Adjustment Notice. For an explanation of the error(s) on your tax return, see Section A, Explanation of adjustment, or
- we were able to refund part of the amount you claimed, but need more information to process the rest. Within 30 days we will send you a letter explaining what we need from you."
