The certification hearing is to determine if the teen's case will be kept in juvenile court or whether he will be tried as an adult.
Utzinger told the judge on Thursday that the hearing will cover sensitive issues, such as the teen's psychological evaluation and his family history.
"[The teen] is already on suicide watch, partly because of the attention this case has garnered," he told the judge.
Utzinger also argued that an open hearing could harm his client's right to a fair trial and the privacy rights of the two children who still live in the family home.
The teen's guardian ad litem, Debra Jensen, argued that if that sensitive mental health information is revealed, there is concern that the teen might harm himself.
"The entire proceeding really should be closed," Jensen said. "It's just not fair to [the teenager] or this process."
But attorney David Reymann, who represents the Salt Lake Tribune and other media outlets, argued that Utzinger and Jensen failed to show "good cause" that the hearing should be closed. Juvenile court proceedings are legally presumed to be open when a child is over 14 years old and charged with what would be considered a felony in adult court.
"He has been charged with double murder," Reymann told the judge. "…He doesn't get to dictate the terms of this proceeding. That's dictated by the law."
Prosecutors have said they want to have the 16-year-old boy's case tried in adult court, but defense attorneys have asked the judge to keep the boy in the juvenile system.
The teen was arrested May 22, 2013, after his mother called 911 to report finding her 4-year-old son dead on the floor of her West Point home, and her then-15-year-old and 10-year-old sons missing. Deputies found the 10-year-old's body in another part of the house. Both victims suffered "penetrating knife wounds," Davis County Sheriff Todd Richardson has said.
Officers later that night found the then-15-year-old walking in Layton, about 8 miles from the crime scene. He was taken to a hospital and then to the Davis County Sheriff's Office interrogation room for what would become a controversial interview.
The teen was held for questioning into the next morning and pressured by four detectives to give statements, even though he refused multiple times and fell asleep twice, his defense attorneys claimed.
Frost in November agreed that the questioning violated the boy's Miranda rights, and said his statements could not be used against him in the case.
Prosecutors have declined to discuss what the boy said or how the loss of those statements would affect their case. But certain other spontaneous statements made by the teen can still be used by prosecutors, according to attorneys and court documents. Also, police have said that traces of blood found on the teen link him to the crime scene.
The teen is being held at the Farmington Bay Youth Detention Center.
The Salt Lake Tribune initially reported the name of the boy in an effort to help police locate him. However, after the teen's arrest, and consistent with the newspaper's policy of not naming juvenile criminal suspects, his name is now being withheld.
The teen has no prior criminal history, according to court officials.