The condition of the injured man, Rafael Reyna, 45, improved this week but investigators have not yet been able to interview him, Capt. Billy Hayes told a news conference.
Reyna was punched around 12:30 a.m. Saturday while leaving a game between the Dodgers and Arizona Diamondbacks that began Friday evening.
Reyna was on a Facetime call with his wife Cristel at the time but that feature does not save a recording of the video, Hayes said.
A witness provided partial descriptions of a man and woman who were believed to be involved but it offered little to distinguish them from the overall crowd — in their 20s, Hispanic, wearing Dodgers attire.
There was no video of the incident, which Hayes indicated occurred quickly.
"What we believe is that they did not know each other; that the incident stems from an incident that occurred contemporaneous to the altercation in the parking lot," Hayes said.
He would not release information about how it started.
"I know how this began but I'm not willing to discuss it at this point in time," he said. "I'm trying to get an independent recollection of either the witnesses or these individuals rather than it be tainted with me putting anything out in the media."
The occupants of a white SUV thought to be involved were cleared, Hayes said.
Reyna had been described as being on life-supports and in a coma after suffering the skull fracture. Hayes said he had since improved.
"As of Tuesday we became aware that Mr. Reyes was removed from the ventilator and that he is breathing on his own and is regaining consciousness," he said.
But he said the family had hired a lawyer who requested that any inquiries regarding the investigation or Reyna's health go through the attorney.
"So at this point in time I'm not sure when we'll be able to interview him, and as you can imagine with head traumas is some inability of people to recall," the captain said.