Peterson, who was convicted of killing his wife 10 years ago, is seeking a new trial based on SBI crime lab mistakes.
A spokesperson for the AG's office said it has agreed to take over contingent upon a continuance so attorneys can prepare.
A hearing in the case had been set for Dec. 5.
Peterson's case is just one caught up in a much publicized squabble between Cline and Superior Court judge Orlando Hudson. Cline had asked Hudson to disqualify himself from the case after she accused him of malicious conduct against her in other cases.
In an appeal filed earlier this year, Peterson - a well-known novelist - claims a SBI analyst lied about evidence that helped secure his conviction in 2003 on a charge he murdered his wife Kathleen.
Kathleen Peterson's body was found at the bottom of a stairwell in the couple's million-dollar mansion Dec. 9, 2001. According to investigators, she was beaten to death with a fireplace poker by her angry husband. Peterson says he didn't do it.