Do I add the amount deducted on the federal back if also taking it on the NY form??
You do not need to add back the federal tuition and fees deduction. Per the IT-272 instructions, taxpayers are allowed both the federal tuition and fees deduction and the IT-272 credit or deduction:
"You can claim the New York credit or deduction even if you claim a federal credit or deduction for qualified college tuition expenses. There is no limit on the number of eligible students for whom you may claim a credit or deduction. You may claim either the credit or the deduction but not both.
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Only expenses for undergraduate enrollment or attendance qualify."
If the student attended more than one college during the tax year, see "NY - Form IT-272 or IT-203-B – Student Attended Two or More Colleges" in Related Links below.