I was married in 2015, and filed jointly. I was divorced for all of 2016 and will be filing single. I received a 1099G for State Income Tax refund that was split with ex

The first question is ask yourself is, "Is my state tax refund even taxable?"

If you two in 2015 (when you filed married joint) did not itemize, then you don't need to report the refund as income. That's because you got no benefit from paying the taxes in the first place (it was buried in the Standard Deduction).

If you two did itemize, then subtract the amount of the Standard Deduction for 2015 (probably $12,600 but it changes if one or both of you were over 65), from your Itemized deductions amount that you reported in 2015. 

Your taxable income is the smaller of this difference and your tax refund.

OK so far?

Now, if you determine that you have taxable income, split only the taxable income amount as determined above between the two of you and report it as "Other Income" which shows up on line 21 of the 1040.

Don't let it bother you that it won't match the actual refund; as you can see from the discussion above, you should report some, all, or none of the refund anyway, even if you weren't divorced.

If the IRS ever writes you a letter about this, you answer them truthfully about what you did and why - so long as you reported the taxable income (if any), there won't be a problem.