No, you do not. You just have to file the Summons/Complaint. Have the other party sign an acknowledgement of service and waiver of appearance and get the divorce granted based on a default. Good luck.
Instructions are online at the court's website: http://www.nycourts.gov/divorce/pdfs/Divorce-Packet-Instructions.pdf. Generally if there are neither children nor property or assets involved, and neither party is requesting alimony (e.g., maintenance), then you do not nee a full settlement agreement drafted. That said, you're encouraged to schedule a consultation with a NYC Divorce attorney for a full assessment.
* If you found my answer to be "HELPFUL," or the "BEST ANSWER," please feel free to mark it accordingly.
If you feel comfortable in doing the papers, feel free to got to the OCA site and get the forms. You might consider a consultation with an attorney to explain things first.
If you found this "helpful" or "best answer," please click it with my appreciation. My response is for educational purposes and does not constitute legal advice nor creates an attorney client relationship which requires all the details and a personal conference.