There is no other half of a tax refund.
If you were to received a federal tax refund and a state tax refund, those refunds are sent separately by separate tax authorities. The IRS sends a federal tax refund and a State sends a state tax refund.
If you received a federal tax refund and the amount received was less than what was on the federal tax return you filed, see this IRS website for federal tax refunds for information - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
Why is my refund different than the amount on the tax return I filed?
All or part of your refund may have been used (offset) to pay off past-due federal tax, state income tax, state unemployment compensation debts, child support, spousal support, or other federal nontax debts, such as student loans. To find out if you may have an offset or if you have questions about an offset, contact the agency to which you owe the debt.
We also may have changed your refund amount because we made changes to your tax return. You’ll get a notice explaining the changes. Where’s My Refund? will reflect the reasons for the refund offset when it relates to a change in your tax return.
Tax Topic 203 - Refund Offsets for Unpaid Child Support, Certain Federal and State Debts, and Unempl... has more information about refund offsets.
