James Holmes in court, July 23, 2012, with public defender Tamara Brady. Image: R.J. Sangosti/Denver Post/Pool/AP Photo

A mysterious early-morning phone call is emerging as a potentially significant piece of the puzzle in an ongoing legal showdown involving accused mass murderer James Holmes.

The University of Colorado Hospital today said an operator received a strange phone call at 12:31 a.m. on Friday, July 20.

The timing is notable because it was only about ten minutes later that police began receiving the first 911 calls about a shooting during a screening of "The Dark Knight Rises" at the Century 16 multiplex in Aurora, Colorado.

When the switchboard operator answered the call, she said there was only silence on the other end, according to University of Colorado Hospital marketing director Brad Fixler.

"There was nothing on the other end," Fixler told ABC News. "Nobody asked for Dr. Fenton or anyone else during the call."

Fixler says the hospital has no way of knowing whether the caller was James Holmes.

Confirmation of the call, however, comes one day after Holmes' public defender, Tamara Brady, suggested in court that Holmes may have tried to reach his psychiatrist just before the shooting started.

During a hearing Thursday in Centennial, Colorado, Brady questioned Dr. Lynne Fenton, the University of Colorado psychiatrist who was treating Holmes for mental illness while he was a neuroscience graduate student.

Brady read a phone number to Dr. Fenton, asking if she recognized it. Fenton said she did: she believed the number was for the University of Colorado Hospital operator.

Brady asked if the number can be used by patients to reach Dr. Fenton after hours. Fenton said yes.

"Do you know whether James Holmes called that number nine minutes before the shooting started?" Brady asked.

"I don't know," answered Dr. Fenton.

Why is this significant?

If it is proven that Holmes placed that call, it will be a key factor in determining if Holmes still had a confidential, or privileged, doctor-patient relationship with Dr. Fenton when the shooting took place on July 20.

Prosecutors are trying to convince a judge that Fenton's relationship with Holmes ended on June 11, 2012.

Court documents filed by prosecutors indicate Holmes was denied access to university buildings on June 12, "after he made threats to a professor at the school" and subsequently began the process of withdrawal from his graduate program.

Fenton testified that she believes June 11 is the date that Holmes was no longer her patient.

If Judge William Sylvester agrees, he might rule that prosecutors can have access to any communications between Holmes and Fenton after June 11, including a package containing a mysterious notebook.

Holmes mailed the notebook to Dr. Fenton on July 19, prosecutors said.

Defense attorneys want to prevent anyone - especially prosecutors - from getting their hands on the notebook and whatever revelations if might contain about Holmes and his alleged crimes. To do that, his public defenders have to prove that Dr. Fenton and Holmes had an ongoing relationship past June 11, which would make the notebook (and any other communications) privileged and off-limits.

Revealing the July 20 phone call to the hospital, legal observers say, might be one way for Holmes' defense team to establish that he was trying to reach out to Dr. Fenton just before allegedly opening fire inside that crowded movie theater, killing 12 and wounding 58.

Arguments over whether Holmes and Dr. Fenton had a privileged relationship were put on hold until the next hearing on Sept. 20, when the judge hopes to decide the issue.

Many legal observers point out that the issue of privilege may eventually be moot if Holmes pursues an expected insanity defense.

"The only defense that Holmes can mount is 'not guilty by reason of insanity,'" said Denver criminal defense attorney David Lane. "Once he does that, the notebook ultimately will find its way into the hands of the district attorney anyway."

In the meantime, on Friday a group of Aurora shooting victims and their families are meeting with officials over a dispute involving more than $5 million in public donations.

At an emotional news conference Tuesday, relatives of some of those killed on July 20 demanded a greater voice in how the money is distributed.