Updated

Jodi Arias returns to court Thursday for the first time since the penalty phase of her case ended in mistrial last month as lawyers discuss plans for a new trial to decide the punishment for the convicted murderer.

Arias was found guilty of first-degree murder on May 8 in the June 2008 stabbing and shooting death of boyfriend Travis Alexander at his suburban Phoenix home. About two weeks later, the same jury failed to reach a unanimous decision on whether to sentence Arias to life in prison or death.

While the murder conviction will stand, the judge set a July 18 date for a new penalty phase, something that could take several months as attorneys put on a mini-trial of sorts to get a fresh jury up to speed on the case. Jury selection alone could take weeks, given the difficulty of seating an impartial panel in a case that has attracted global attention.

The hearing Thursday could address the timing of a potential new trial. Arias' attorneys have asked to resume the case in January 2014 because of scheduling conflicts and the need to prepare a new case. Prosecutors believe the new penalty phase could begin at the end of July.

Another lingering question is whether prosecutors will go forward with their pursuit of the death penalty.

Prosecutors have the option of taking the death penalty off the table, and the judge in that case would then sentence Arias to one of two punishments: life in prison or the more unlikely life in prison with the possibility of release after 25 years.

Maricopa County Attorney Bill Montgomery said last week his office is continuing to prepare for a retrial aimed at securing a death sentence. He had previously said he is confident an impartial jury can be seated to determine Arias' punishment but added that he is open to input from defense lawyers and the victim's family about possibly scraping a new trial in favor of a life sentence for Arias.

Meanwhile, after losing motions for mistrials, appeals to higher courts and efforts to quit the case altogether, Arias' attorneys tried a new tactic this month, appealing to the court of public opinion while hoping to influence Montgomery's decision.

"It is solely for them to determine if continuing to pursue a death sentence upon Ms. Arias, who is already facing a mandatory life sentence, is a good and proper use of taxpayer resources," defense attorneys Kirk Nurmi and Jennifer Willmott wrote in a statement provided to The Arizona Republic.

Taxpayers footed the bill for Arias' court-appointed attorneys at a cost so far of nearly $1.7 million, a price tag that will only balloon if the case moves forward.

Under Arizona law, if prosecutors insist on pursuing death, a new panel must be seated to determine a sentence. If another deadlock occurs, the death penalty would automatically be removed, leaving the judge to sentence Arias to one of the life-in-prison options.

Arias, 32, admitted she killed Alexander, but claimed it was self-defense after he attacked her. Prosecutors argued it was premeditated murder carried out in a jealous rage after the victim wanted to end their affair and planned a trip to Mexico with another woman.

Arias stabbed and slashed Alexander nearly 30 times, slit his throat so deeply she nearly decapitated him and shot him in the forehead. She then left his body in his shower where friends found him about five days later. She testified for 18 days during her four-month trial, describing for jurors an abusive childhood, cheating boyfriends, dead-end jobs, a shocking sexual relationship with Alexander, and her contention that he had grown physically abusive.

She said she recalled Alexander attacking her in a fury after a day of sex on the day he died. She said Alexander came at her "like a linebacker," body-slamming her to the tile floor. She managed to wriggle free and ran into his closet to retrieve a gun he kept on a shelf. She said she fired in self-defense but had no memory of stabbing him.

Arias acknowledged trying to clean the scene of the killing, dumping the gun in the desert and working on an alibi to avoid suspicion. She said she was too scared and ashamed to tell the truth. However, none of Arias' allegations that Alexander had physically abused her in the months before his death and that he owned a gun were corroborated by witnesses or evidence during the trial. She acknowledged lying repeatedly before and after her arrest but insisted she was telling the truth in court.