The filings came the same day the judge overseeing the trial worked to whittle down the pool of more than 1,000 potential jurors, excluding people who said they believed Hernandez was guilty, expressed a bias against people with tattoos or who said it would cause a hardship for them to serve on a trial expected to last more than a month.
Hernandez has pleaded not guilty to the June 17, 2013, slaying of semiprofessional football player Odin Lloyd, 27, who was dating the sister of Hernandez's fiancee.
Prosecutors say Hernandez and two other men, Carlos Ortiz and Ernest Wallace, picked Lloyd up at his home in Boston's Dorchester section and took him to an industrial park near Hernandez's home in North Attleborough, where he was shot to death. Prosecutors have not said who they believe pulled the trigger, although they have said they believe it was orchestrated by Hernandez.
Investigators say the murder weapon was never found.
In filings released by the court late Thursday afternoon, Hernandez's lawyers said he has a right to know if his fiancee, Shayanna Jenkins, has made any deals. The two have a daughter together. Prosecutors last week petitioned Garsh to grant Jenkins immunity to testify. The court has not said whether it was granted.
Jenkins has pleaded not guilty to perjury for allegedly lying to the grand jury investigating Lloyd's killing. Prosecutors have said Jenkins lied dozens of times, including when she said she couldn't remember where she disposed of a box from the basement of their home that Hernandez allegedly told her to get rid of.
Jenkins' lawyer did not immediately return an emailed request for comment.
Hernandez's lawyers also asked the judge to let them call David Greenblatt, a doctor who is an expert in PCP. Both sides have said Wallace and Ortiz were seen smoking PCP on the night of June 15, 2013. Prosecutors previously opposed calling Greenblatt as a witness, saying his testimony will be irrelevant because the two smoked the PCP more than 27 hours before the killing happened.
Greenblatt says in an affidavit filed with the court that symptoms of PCP psychosis can include aggressive or violent behaviour, homicidal tendencies and impaired memory. He also says the symptoms can last for many days.
Ortiz and Wallace have pleaded not guilty to murder charges. Their cases have not yet gone to trial.
Hernandez was in court on Thursday as Garsh, along with Hernandez's defence team and prosecutors, reviewed prospective jurors' written questionnaires. The sides raised concerns about hundreds of prospective jurors, referring to them by their juror numbers.
One prospective juror answered that Hernandez was their favourite player. Assistant District Attorney William McCauley said that raised the question of whether the person could be fair and impartial, but defence lawyer Michael Fee said it could just be that the person admired Hernandez, and that does not disqualify them. Garsh agreed to bring the person in for further questioning.
She is expected question individual jurors starting Friday.