(CNN) -- Aaron Hernandez's fiancee pleaded not guilty to perjury on Tuesday, with prosecutors alleging she lied to those looking into the death of Odin Lloyd, whom Hernandez is accused of killing.
A lawyer for Shayanna Jenkins strongly denied the claims in a Fall River, Massachusetts, court, saying her client has been "fully cooperative other than insisting on her Fifth Amendment rights" and received immunity for grand jury testimony. Jenkins is among a handful of people charged as investigators look into Lloyd's fatal shooting in June. Hernandez has pleaded not guilty to first-degree murder in Lloyd's death.
"It seems to me that this is overreaching, the indictment is overreaching, the statement by (the prosecutor) is overreaching, and the request for bail is overreaching," said Jenkins' lawyer, Janice Bassil.
She spoke after Bristol County Assistant District Attorney Patrick Bomberg presented a case against Jenkins.
Among other things, Bomberg alleged Jenkins destroyed evidence -- a box that Hernandez, who until earlier this year was a standout tight end for the New England Patriots, asked her to find in his North Attleborough, Massachusetts, home and "get rid of." Jenkins then left her home with a black trash bag and returned sometime later without it, the prosecutor said.
"She told her sister that she was going to the bank, she told her uncle ... she was going to the store, she told the grand jurors that she was going to get baby formula," Bomberg said.
Asked where she did go, the prosecutor said Jenkins told the grand jury she "didn't know where she went" and she couldn't remember what Hernandez asked her to dispose of.
Jenkins testified she tossed the trash bag in a Dumpster, though she couldn't say where that Dumpster was, Bomberg said.
Speaking on this point, Jenkins' lawyer said her client "received immunity on all of these things they are accusing her of" and, even then, she didn't lie to the grand jury. At that time, Bassil said, Jenkins was subject to "heavy-handed questioning" during an "extremely difficult" period when Hernandez, the father of her young child, was under arrest for murder.
Bassil described the relationship between Hernandez and Jenkins as "don't ask, don't tell."
"She could spend her life tracking him down and asking where he was every single minute, or she could choose to say what you do on your own time is your own time," the lawyer argued. "If you didn't do this, you didn't do this. I don't need to know any more detail."
Bomberg, the prosecutor, also said that Jenkins lied to police when she told them Lloyd was a drug dealer.
Jenkins "corrected that in the grand jury" testimony, Bassil said, stating that while she knew Lloyd provided marijuana to Hernandez, "she had no other evidence" that he dealt drugs.
After Tuesday's hearing, the judge denied the prosecution's request for $5,000 bail and instead released Jenkins on her own recognizance pending trial. The next hearing in her case is set for November 6.