I got a 1099g for the 2015 tax year. Box 2 on this form says it is state or local income tax refund, credit or offsets. How do I file this?

If you itemized your deductions on your 2015 Federal income tax return AND you took a deduction for the state income taxes that you paid in 2015, then you need to report it as income on line 10 of your 2016 Federal Form 1040. Although this income is reportable and subject to tax, that doesnt mean that it will be included in your taxable income. It depends on your specific situation. 

Please refer to pages 23-24 of the IRS Form 1040 instructions under the headings, "line 10: taxable refunds, credits, or offsets of state and local income taxes" and "state and local income tax refund worksheet - line 10" for additional information. https://www.irs.gov/pub/irs-pdf/i1040gi.pdf

Please refer to the following FAQ for instructions on how to enter your 1099G form. https://ttlc.intuit.com/replies/4768356

 However, if you did NOT itemize your deductions on your 2015 Federal income tax return OR if you itemized deductions but did NOT take a deduction for state income taxes paid in 2015,  then you would NOT report this on your 2016 Federal tax return.