I received 1099-G.Do I have to claim my 2015 state tax refund

Yes.  It may or may not be taxable.  To enter a state refund just type  1099-g (with the dash)  in the search box at the top of your return and click on Jump To it.

OR  Enter the 1099G under
Federal Taxes Tab
Wages & Income
 
Scroll down to  Other Common Income
      You might need click on Show More to expand the section

Then it's the first line for Refunds Received for State/Local Tax Returns - Click Start
     You do not want the next line that says Other 1099G Income
 
On the first screen check YES - Received a State Refund.

Enter the amount and continue on and after a couple screens, it will ask you a couple questions to determine if it's taxable.  It may or may not be taxable.  It is taxable if you itemized deductions the year it is from.  If you took the standard deduction it is not taxable. If you filed form 1040A or 1040EZ you took the standard deduction and don't have a schedule A, so the refund is not taxable.