After you file

Maybe not

That can happen in certain situations (a lower amount on line 10 of the form 1040).  IF the itemized deductions that were used in the prior year were close to the Std Deduction that you could-have used in 2016, then the amount of refunded state taxes that show up should only be the amount required to take you down to the Std Deduction level for that year.

Example: say you filed MFJ in 2016, and had $13,000 of itemized deductions, including maybe 3,000 state income taxes paid as a part of those itemized deductions...….and you then received a $900 state 2016 refund, after filing in 2017.    Since the Std Ded for a MFJ tax return (under age 65) was 12,600 for 2016 taxes ….only $400 of that $900 should show up on line 10 of the 2017 form 1040.   i.e. just the amount that would bring the 13,000 itemized, down to the 12,600 Std Ded. for a MFJ couple.

The tax software does this calculation, as long as all the proper income and deduction $$ carried into 2017 from your 2016 file (Or you entered the 2016 $$ correctly during the interview if you didn't have a 2016 tax file to transfer into your 2017 file)
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*