Park is charged with the murder of 21-year-old aspiring actress and model Juliana Redding of Arizona.
Redding's body was found on March 16, 2008, in her rented condominium on Centinela Avenue near Santa Monica Boulevard.
Police were called to her apartment when Redding's mother contacted authorities and informed them that she couldn't reach her daughter.
The connection between Park and Redding may be money. According to published reports, Park was paid $250,000 three weeks before Redding's murder and another $113,000 just days before Park's arrest on June 18.
The money allegedly came from Park's employer, a Marina del Rey doctor who was involved in a failed business deal with the victim's father.
The doctor's attorney said he is out of the country and can't be reached.
The prosecution requested that Park's bail be raised from $1 million to $5 million. The judge, however, decided to not allow Park to post bail at all after explaining that bail information is not supposed to be released to the public until a hearing takes place.
"You can't be allowed until a hearing is rendered, because I have to make a finding that if you do seek to bail out, that the source of the funds is a legitimate source of money," the judge explained in court.
Park's family and supporters had no comment as they left the courtroom.
Redding moved from Arizona to Santa Monica to pursue her dream of acting and modeling. She had a small movie role in 2005 and was photographed for Maxim, winning one of the magazine's "Hometown Hotties" contest.
Park's arraignment has been postponed until July 6. She faces 25 years to life in prison if convicted.
Santa Monica police said there may be other charges in the case.