Do I need to amend my state tax return to obtain the $10,200 UE exemption?

When you do your taxes in TurboTax, your AGI with the $10,200 deducted will be transferred to the state return.  If the state has not yet determined whether they will forgive the income tax on the first $10,200 of unemployment, then you will not be able to e-file that state until the issue has been resolved.

IRS $10,200 unemployment exclusion

Unfortunately I've already filed both Federal and State before the exemption was made. Turbotax advised the Federal form will automatically be updated, but no word as to what I need to do with the Missouri State income tax I already filed.

The program is still being updated for Missouri.

I recommend checking the link below periodically for updates.

State tax treatment of unemployment