The IRS will start issuing refunds in May from unemployment if you are eligible. As far as the state is concerned you need to contact your tax representative.
American Rescue Plan makes $10,200 of unemployment from last year nontaxable. If you have already filed do not worry. The IRS says they will fix the return and start issuing refunds in May.
When it comes to your state refund it can become a bit tricky. Most states have decided to adapt the federal unemployment refund rules. However, you will have to file an amended return with the state in order to receive an additional refund.