It depends. If it is taxed in New York State and you are a New York City resident, then it would be taxed on the state and local level.
In most cases, New York state employers withhold disability premiums from an employee's pay. In this case, your disability income is not taxable. However, if you did not have a SDI deduction from your pay, or paid for a percentage of it, then it would be fully or partially taxable.
A good place to start would be your previous W-2's in Box 14 for this employer. Does a SDI deduction show up in this box? If so, confirm with your employer if you paid for the full premium or just a portion of it.
With all that being said, if it was taxable (either partially or completely), you should have gotten a 1099 for it.
Thanks so much for your response but I still need help in regards to this situation. Are you able to assist me with the filing or does Turbotax pick someone at random to help me with my filing?
Once you enter all of your forms, you can ask for a line by line review to walk you through and make sure it is right. See What is a Line by Line Review?