Can I use box 12 DD for my 'contributions to a High Deductible Health Plan' when preparing my GA state tax return?

No, the Georgia High Deductible Health Plan deduction includes only the HDHP premiums that are not already accounted for on the federal return.

However, since the HDHP premiums are normally not taxed at the federal level (they are reported with code "DD" in box 12 on the W-2), you don't need to enter them on the Georgia return, because this effect carries through to the Georgia income for state purposes from the federal return.

Therefore, you are unlikely to need to enter anything in this field on the Georgia return.

The Georgia instructions say

"The amount [for the premium and HSA expenditures] may only be deducted to the extent the deduction has not been included in federal adjusted income and the expenses have not been provided from a health reimbursement arrangement and have not been included in itemized deductions." See the Georgia instructions.