Unfortunately, the answer to your question is no. The amount shown on your W-2, Box 12, using Code DD, represents the of the cost of pre-tax employer-sponsored health coverage, and is for your information only. The amount reported with Code DD is not taxable, but neither can it be claimed as a tax deduction (medical expense) by an individual taxpayer. This fact would be true whether you work for the NYC department of education, or if you worked in the private employment sector. The tax rules are the same here.
You can read more about Code DD, if you would like, at the following TurboTax FAQ webpage:
also please see the IRS instructions for W-2, Box 12, Code DD, as found on Page 20 of this official government document:
Thank you for asking this important question.