However, taxpayers would have to file an amended return if they did not originally claim the EITC or other credits, but now are eligible because the [unemployment comp] exclusion changed their income. These taxpayers may want to review their state tax returns as well.
IRS to recalculate taxes on unemployment benefits; refunds to start in May | Internal Revenue Service
See these re State:
How is my state taxing unemployment income? (intuit.com)
Do I need to amend my state return to update my un... (intuit.com)