Moved my family from N.H to G.A at the end of Nov. I continue to work for the same company since I have been working from home the last 6 years.

Do I file GA Taxes?

I usually do my own taxes using TurboTax, this year I not sure if I have to file for both states NH and GA, I also made some home improvements in order to sell the house which could qualify for Tax deduction (energy efficient garage doors)... I also should qualify for tax credit because of the purchase of our new home in GA since I lived more than 8 years on my previous home and the new home is definitely a step up...

Anyway, I know I dumped a few things here, so the main question is. Considering all of these:

Do I file in NH and GA Taxes?

And considering the move and the things I want to report, do I need to see a Tax accountant or could I handle it with TurboTax?

Thanks in advance

Yes, you file GA taxes as a part-year resident, covering the period Nov 1 - Dec 31. Presumably since Novenber your employer has been withholding GA income tax from your pay, right?

NH doesn't have income tax, so why would you file there?

TurboTax should be fine - try it and see if it properly captures the credits that you mentioned. It should also be able to handle the part year return for GA without a problem, although you'll need to purchase the GA tax module. Others on this site would probably suggest using a Pro, as the cost difference between professional preparation versus buying TurboTax federel and state programs may not be too much.