Oral arguments are scheduled for Tuesday in Jackson.
Goodin is appealing an adverse 2010 ruling from Newton County Circuit Judge Marcus Gordon, who found Goodin mentally competent and denied his motion for a new trial.
The Supreme Court granted Goodin a hearing in 2009 on claims of mental disability and ineffective work by his case lawyer.
Those post-conviction claims were initially dismissed by Gordon in 2007. In such claims, an inmate argues he has found new evidence — or a possible constitutional issue — that could persuade a court to order a new trial.
Goodin was convicted of capital murder in 1999 in the death of a Union, Miss., shopkeeper.
What prompted the Supreme Court to order a mental disability hearing for Goodin was his claim that his former attorney failed to call for testimony any of the psychiatrists who had diagnosed Goodin as schizophrenic, and that the attorney failed to present records showing the diagnosis of schizophrenia to the trial court.
Goodin also claimed records attesting to his poor academic performance and inability to hold a job should have been introduced.
He claimed his due-process rights were violated because the trial judge ruled on the competency petition without evidence of schizophrenia and low intelligence being introduced.
The Supreme Court ruled in 2009 a hearing was necessary because Gordon, the trial judge, through no fault of this own, wasn't presented with the evidence needed to decide the mental disability issue.
The legal work of Goodin's former attorney, Robert Ryan, had been called into question before. Attorneys for Mississippi death row inmate Dale Leo Bishop claimed Ryan — former head of a state agency responsible for representing indigent death row inmates on appeal — suppressed evidence of a bipolar disorder and intentionally sabotaged the case.
Bishop was executed in 2008 after the U.S. Supreme Court declined to take up his final three appeals.
At Goodin's trial, records show a surveillance tape played in court depicted Goodin entering Rigdon Enterprises in Union on Nov. 5, 1998. He is seen on the tape stealing money from the cash register as well as taking a VCR and videotape.
The tape also showed 64-year-old Willis Rigdon raising his hands as he was led at gunpoint from the store and forced into his pickup truck.
Rigdon was shot with a pistol after a short trip down a nearby dirt road. He was dumped in a ditch and died later at a hospital.