If I live/earned wages in GA for 2020, but had to file for Unemployment in MA (because I was working there in 2019), do I still need to file for nonresident state tax?

Yes. You will file a non-resident Massachusetts income tax return. MA nonresidents are subject to Massachusetts income tax on unemployment compensation that is related to previous employment in Massachusetts.

Georgia will give you a tax credit for taxes paid to MA.

See Learn about tax treatment of unemployment compensation.

Thank you for your reply!  How do I go about filing that nonresident form?  Is it on the MA DOL website or do I need to file my GA taxes first?  

You can prepare the Massachusetts non-resident return and the Georgia resident return in TurboTax. It’s important to do both in TurboTax so TurboTax can give you the proper credit on your GA return for MA tax paid.

Finish your federal taxes. Then prepare the nonresident. Then the resident return.

Here’s the link: How do I file a nonresident state return?

Got it!  Thanks so much for your help!!