Carlos Medina (63) is charged with the murder of Bishop David O'Connell (69) who was shot dead in his Los Angeles home in February 2023.
Medina of Torrance in LA County previously pleaded not guilty to one felony count of murder.
He was first arraigned at Foltz Criminal Justice Centre in downtown LA in February of last year.
The 63-year-old has also been charged with using a firearm during the commission of an offence.
The legal team for Medina told a recent pre-trial hearing in LA that they were concerned about his fitness to stand trial having been charged with the murder.
If he is found to be mentally incompetent he will be treated until he is deemed fit.
Lawyers for the accused did not suggest that he was mentally incompetent during the period where the alleged offence occurred.
Medina is due back before Hollywood Superior Court on October 31.
The handyman - whose wife was the housekeeper for the Cork-born bishop - faces two charges, one of felony murder and a special charge of using a firearm while committing a crime.
Medina, who is also known as Carlos Medina-Vallejo, has denied the murder charge and a full trial will now be staged in Los Angeles.
The trial - expected to prove one of the highlight profile murder cases in Los Angeles - may not be scheduled until late 2025.
Los Angeles County District Attorney George Gascón outlined the prosecution case against Medina who, the State alleged, used a .38 calibre revolver to fatally shoot the well-known cleric.
Prosecutors contend that forensic evidence indicated the Irish bishop was asleep when he was confronted and shot.
Medina pleaded not guilty last March to the felony count of murder.
The accused, who has an address in Torrance County in LA, was first arraigned at Foltz Criminal Justice Centre on February 22, just two days after he was first arrested over the killing.
Medina faces a 35 year prison sentence if convicted.
Convictions for felony murder, with aggravating circumstances, can carry a maximum sentence of life imprisonment without parole.
Los Angeles held three days of mourning for Bishop O'Connell last February with the killing having shocked a city notorious for gun related violence.
Bishop O'Connell died from a gunshot wound to his upper chest after being found at his residence on Saturday, February 18.
He was found lying on his bed at his residence in east Los Angeles off Janlu Avenue in the Hacienda Heights area shortly before lunchtime when a church deacon went looking for the cleric after he failed to turn up at an arranged meeting.
Police believe Bishop O'Connell was asleep in bed when attacked with no sign of forced entry.
The fatal shot was fired from a medium calibre handgun, a .38 Special.
Medina had previously undertaken gardening and small duties at the cleric's Hacienda Heights home in east Los Angeles.
He was arrested by armed police within 48 hours of the killing following a lengthy standoff at Medina's home in Torrance, a short distance from the cleric's property.
Bishop O'Connell's death shocked the Los Angeles community with the Irish cleric known as 'The Peacemaker' for his courageous work to end gang violence and protect vulnerable migrants.
He was known to neighbours and friends as 'Bishop Dave' and was renowned for his humility and aversion to pomp and ceremony.
The Cork cleric earned the title 'The Peacemaker' when he bravely helped broker a peace deal during the 1992 Los Angeles riots which erupted in the wake of the police beating of African-American motorist Rodney King.
He put his own life at risk in going into riot-ravaged areas to negotiate directly with gang leaders.
Bishop O'Connell focused his ministry on trying to help the poor and marginalised in society.
He was renowned for his work with migrants and particularly those stranded in the large migrant camps around Los Angeles.
Ordained in Ireland in 1979, Bishop O'Connell spent his entire ministry in Los Angeles though he was a frequent visitor back to Ireland.
He was made an Auxiliary Bishop of Los Angeles by Pope Francis in 2015 in recognition of his work with the poor and vulnerable.
His Requiem Mass was led by Archbishop Jose Gómez and was celebrated at the Cathedral of Our Lady of the Angels.
Archbishop Gómez recalled how Bishop O'Connell spoke fluent Spanish but with a distinct Irish accent.
"He was a good friend of Los Angeles - he was a good priest, a good bishop and a man of peace. His death is a terrible loss."
The Requiem Mass followed special vigil Masses at the Church of St John Vianney in Hacienda Heights and the Cathedral of Our Lady of the Angels.
A seven hour public viewing also took place at the cathedral for friends, colleagues and parishioners.
A special memorial Mass was also celebrated in his honour in his native Cork.
The cleric regularly brought California church groups back to Cork.
Bishop O' Connell is survived by his brother Kieran, his sister in law Paula and his nieces and nephews.