Which taxpayer is responsible for reporting last years state refunds as income on their federal tax return if your filing status has changed from married filed jointly to head of household this year?
If you itemized your deductions on Schedule A last year and need to include your 2017 State Tax refund as income on your 2018 Tax Return, you can split the refund between you and your spouse in any way that you agree upon. You can claim 100% of the state refund, you could each claim 50%, or use any other allocation % you both consider fair. As long as the full amount gets reported, the IRS allows you to split the reporting of the State Refund from the 1099-G between the two of you any way you would like.
In most cases, Ex-Spouses each report 1/2 of the refund to keep things simple. However, feel free to agree on splitting it in whatever way seems fair to both of you.
Note: If you didn't itemize your deductions on Schedule A in 2017, your State Tax Refund does not need to be reported as income on your 2018 Tax Return.