The justices say it appears the trial judge adopted findings submitted by prosecutors. The justices say they want the judge to put the findings into his own words.
Chase was convicted and sentenced to death in 1990 for the Aug. 14, 1989, killing of 70-year-old vegetable salesman Elmer Hart in Copiah County.
Authorities said Hart apparently arrived at home as his wife was being robbed by Chase and another man.
Prosecutors say Hart's wife had been doused with an ammonia-like substance and tied up and gagged. They say she watched helplessly as her husband was shot.
Hart's body was found on a bedroom floor beside his wife.
The state Supreme Court upheld Chase's sentence in 1994.
In December, Chase's attorneys said in a post-conviction proceeding that Chase had argued that a pretrial mental examination showed he was mentally incapacitated. Attorney Jim Craig said Chase was examined by two doctors. But court records show one doctor did not find him mentally disabled.
Craig said one of the doctors who examined Chase gave "a seat-of-the-pants judgment about the intellectual functioning of the defendant," which Craig argued was wrong.
Craig said people had testified that Chase, as an adult, lacked the mental capacity to perform simple tasks like choosing his own clothes.
Craig argued the evidence was enough to justify throwing out the death sentence.
State prosecutors told the court there's no proof to back up Chase's claim.
"The evidence is there to support the fact that he is not mentally retarded," Assistant Attorney General Marvin White Jr. told the court.
In 2010, Circuit Judge Lamar Pickard in Copiah County ruled against Chase's claims of mental disability.
In an order issued Jan. 17, Supreme Court Presiding Justice Jess Dickinson said Pickard must resubmit his findings to the Supreme Court and provide reasons why he denied Chase's petition.
Dickinson said the Supreme Court also wanted to make sure that mental health experts were allowed to render opinions to the trial court on testing done on Chase by other doctors such as those at the Mississippi State Hospital in Whitfield.
In a post-conviction petition, an inmate argues he has found new evidence — or a possible constitutional issue — that could persuade a court to order a new trial.