| You can agree to have one spouse report the entire state tax refund as taxable income, thus the 1099 would agree to the IRS reported amount of the tax refund. Clearly, this would not trigger an IRS inquiry!
Alternatively, both of you and your ex-spouse can agree to share 50% of the tax refund, and report this amount on your respective tax return.
The key factor is that together both of the spouses are reporting as taxable income the entire amount of the Tax Refund, assuming of course you had itemized the prior year. | 
