Is a New York state school tax refund check taxable if I did not itemize deductions on my Federal Tax return ?

No.  In general, if you didn’t deduct state and local income taxes last year, you don’t need to pay taxes on your state and local tax refund this year. For instance, if you didn’t itemize your deductions last year (you took the standard deduction) then your state tax refund is tax-free this year.