Yes, you can divide it in half if you filed Married Filing Jointly (MFJ) the previous year.
If you filed Married Filing Separately (MFS), then you and your former spouse will receive separate forms and you will only be responsible for the refund amount on your 1099-G or separate state return.
Note: Your divorce decree may state specific amounts to be divided between you and your former spouse on your tax return. If so, you should follow the divorce decree.
If you did not itemized your deductions for the prior year, the refund is not taxable to you.