You would need to file a separate Kentucky state return This is copied from Kentucky's website:
Filing as an Injured
Spouse on Your
Federal Form 1040?
Kentucky does not recognize the federal injured spouse form. Income tax
refunds may be withheld by the department if you owe money to the Kentucky
Department of Revenue, another state
agency or the Internal Revenue Service.
Kentucky law requires the offset of the
entire refund if a joint return is filed. If
spouses want to keep their tax liabilities and/or refunds separate, each must
file a separate tax form. If you choose
to file separately on a combined return,
for agencies other than the Department
of Revenue, the refund will be apportioned between spouses, based on
each spouse’s income. The indebted
spouse’s refund will then be paid to the
appropriate agency
