Cline had asked for a delay so that the North Carolina Attorney General's Office could take over the case.
A spokesperson for the AG's office said last week it has agreed to take over contingent upon a continuance so attorneys could prepare.
Peterson, who was convicted of killing his wife 10 years ago, is seeking a new trial based on alleged SBI crime lab mistakes.
In an appeal filed earlier this year, Peterson 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.
Peterson's case is just one caught up in a much publicized squabble between Cline and Judge Hudson. Cline has accused the judge of malicious conduct against her, but lost her bid Monday to have him removed from the case.
Judge Carl Fox Monday said affidavits presented by Cline did not prove her claims.
In court Tuesday, Cline brought in Kathleen Peterson's sister to address Judge Hudson. She made an emotional and passionate plea a delay, saying it was obvious the DA's office wasn't prepared to defend the rights of her deceased sister.
Despite the plea, Judge Hudson denied the request to continue.
DA Cline then asked the court to reconsider its decision, allowing enough time for Special Prosecutor Jim Coman to come to the courthouse to speak to Judge Hudson.
He denied her request again.
Then just as the hearing got underway, a bomb threat cleared the courthouse.
After a delay, the hearing resumed again. It's expected to last about two weeks.