On this website, I do not always get to give good news, and this is one of these times.
This is not public information. The former employer has discretion whether to disclose the reason in New York. The standard is that the employer will confirm former employment and provide the dates, but anything else they say beyond that is up to them. Many employers will not say anything else, for fear of being sued for defamation by the employee (regardless of whether the reason for termination was legitimate or not - they'd simply rather not take the chance).
So one can ask, but it is completely and wholly up to the former employer to disclose anything.
Please note: If I tell you simply what you wish to hear, this would be unfair to you. I need to be honest with you and sometimes this means providing information that is not optimal. Negative ratings are reserved for experts who are rude or for erroneous information. Please rate me on the quality of my information; do not punish me for my honesty.
I hope this helps and clarifies. Please use the SEND button to keep chatting, or please RATE when finished. You may always ask follow ups at no charge after rating. Kindly rate my answer as one of THREE OR MORE STARS and then click FINISH to submit that rating, as this is how experts get credit for our time. Rating my answer the bottom two stars (or failing to submit the rating) does not give me credit and reflects poorly on me, even if my answer is correct. I work very hard to formulate an informative and honest answer for you; please reciprocate my good faith with a positive rating (it does not cost anything extra to rate).