Most returns are processed and the refunds deposited within the first three weeks after filing your return.
The state of Ohio is currently working on a change in their tax law that will exclude the income tax on the first $10,200 of unemployment benefits for people who qualify. Until that law is passed and implemented into TurboTax you will not be able to e-file the Ohio return.
When that change has been made to TurboTax, you will be able to e-file Ohio.
You can check the status of your federal refund at the IRS Where's My Refund? site.
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