It is highly unlikely that the TurboTax program made the error. That's because a programming error in the New York software would have affected tens of thousands of users, which did not happen.
As @Critter-3 said, if you are sure your NY return was incorrect, you should carefully go through the amendment process and submit an amended return. If there was an error, you should come across it during the amending process. Remember that amended returns must be printed and mailed; they can't be e-filed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
