O.C.G.A. § 48-7-29.2 provides for a qualified caregiving expense credit. This is a credit of 10 percent of the qualified caregiving expenses for a qualifying family member. The credit cannot exceed $150. The requirements are as follows:
1. Qualified caregiving expenses are defined as home health agency services, personal care services, personal care attendant services, homemaker services, adult day care, respite care, or health care equipment and other supplies which are determined to be medically necessary by a physician.
2. Qualified caregiving expenses do not include expenses that were subtracted to arrive at Georgia net taxable income or with respect to any qualified caregiving expenses for which amounts were excluded from Georgia net taxable income.
3. The caregiving services must be purchased or obtained from an organization or individual not related to the taxpayer or the qualifying family member.
4. The qualifying family member must be at least age 62 or be determined disabled by the Social Security Administration. A qualifying family member is defined as the taxpayer or an individual who is related to the taxpayer by blood, marriage or adoption.
5. There is no carryover or carry-back available.
6. The credit cannot exceed the taxpayer's income tax liability.
From looking at the Georgia Form 500 it does not appears that you claim the Georgia child and dependent care expense credit by submitting the appropriate Federal child care credit schedule.
From the above descriptions, it does not seem that you can claim both credits for the same expenses. But, there does not appear to be any reason that you could not claim the one credit that is most beneficial for a given amount of expense or, that you could not claim both credits in relation to different expenses. For example, if your expenses exceed the maximum amount that is allowed for credit on the federal dependent care credit it does seem you can use those expenses not claimed for federal purposes for the Georgia credit.
I hope this helps.