The outcome of the issue before state District Judge Terry Ruckriegle could play a huge role at trial: The defense hopes to argue the woman had mental problems that could have clouded her perception of what happened between the two in a Colorado hotel room last June. Bryant has insisted they had consensual sex.
CBS News Correspondent Lee Frank reports Bryant's defense team is also trying to attack the credibility of the alleged victim, hoping her medical records will show a "pattern of attention-seeking conduct."
Ruckriegle asked attorneys on both sides to spell out in briefs whether the medical history should be allowed. He said the issue would be taken up again at a Jan. 23 hearing.
Prosecutors and attorneys for the woman say her medical history should remain out of public view. They urged the judge to hold any arguments about the issue behind closed doors, and he agreed.
Among those subpoenaed by the defense to appear Friday were the alleged victim's mother and a former friend, Lindsey McKinney, who has said the woman tried to kill herself twice this year. The woman's father, who was not subpoenaed, spent the day sitting in the gallery, 20 feet away from Bryant.
The 25-year-old Los Angeles Lakers guard faces four years to life in prison or 20 years to life on probation if convicted of felony sexual assault. The Lakers had a home game Friday night, but it was unclear whether Bryant would be able to return to California in time.
In Colorado, medical records must remain sealed unless the patient consents or gives up their privacy rights. Bryant's lawyers contend the woman waived those rights because she spoke with others about her medical condition.
Specifically, the defense wants access to documents from the North Colorado Medical Center in Greeley, where authorities brought the woman in February after determining she was a "danger to herself." She was a college student in that city at the time.
Defense lawyers contend in court filings that Bryant's accuser tried to kill herself in February and again in May, and accused Bryant of rape to get an ex-boyfriend's attention. They also say she had been prescribed an anti-psychotic drug.
The defense also wants access to the notes of a rape victim's advocate who spoke with the woman. The judge agreed to hear arguments on that issue, perhaps as early as Friday.
Deputy prosecutor Ingrid Bakke said allowing the medical details to be brought up before a national media audience would prevent other alleged sexual assault victims from coming forward.
"When the bell is re-rung, it revictimizes the victim," she said.
John Clune, an attorney representing the woman, said her rights should be protected just as much as Bryant's were during a preliminary hearing in which his statement to investigators was played behind closed doors.
Any testimony on the medical issues should be kept secret unless the judge decides it can be used at trial, he said.
Sitting out the argument was Bryant's defense team. Attorney Hal Haddon said Bryant would like the entire hearing closed to the public, but he did not weigh in specifically on the woman's medical history.
Tom Kelley, an attorney representing media organizations including The Associated Press, told the judge a significant amount of information about the woman's medical and psychological history already has been reported and only details that have not been publicized should be kept secret.
"Unless someone gives graphic detail of what's in a medical record, I don't think it could be seriously argued" that the hearing should be closed, Kelley said.
The hearing began with the judge rejecting a prosecution request for an investigation into media leaks, saying it would be a waste of time.
The defense also asked Ruckriegle to order authorities to turn over some evidence to an independent laboratory for DNA testing. Legal experts have said the evidence is probably blood, pubic hair and semen samples found during a hospital examination of Bryant's accuser.