Do I have to report NY family relief tax credit and empire state child credit as income on my 2017 federal tax return?

No. You will receive form 1099-G from the state of New York reporting your state refund, if applicable. This is what you will report on your current tax return.

I imported my TurboTax 2016 return into TurboTax 2017. After importing, my Fed 1040 box 10 "Taxable refunds, credits, or offsets of state and local income taxes" shows $350 less than the actual NYS refund I received for tax year 2016. Is this because the NY family relief tax credit is not taxable on my Fed return for 2017?