Brad Bernheim, the building manager says the elevator was not operating, but had been secured so no one could enter it.
"I don't know why he was there. That's what we're investigating, how he got down there," Bernheim said. "Yeah, it's strange. You don't normally find bodies in the elevator shafts."
Police say Kliman fell after summoning the elevator.
The investigation will focus on how secure the elevator was, and if it was possible for a person to open the elevator door when the elevator wasn't there.
Kliman is believed to have fallen down the shaft Tuesday evening, but his body was not found until workers showed up to repair the elevator Monday.
Friends said Kliman was a leader in the Pro-Israeli movement. He would often show up at anti-Israel protests to argue his point of view.
"The circumstances are suspicious and certainly those of us who are involved in Israel advocacy are concerned because he was a very very public face of Israel advocacy," said Mike Harris, a friend of Kliman. "He was definitely not afraid to speak up for what he believed in. He definitely had this tendancy to not back down from confrontations. Dan was a passionate advocate for Israel as a jewish state. He was pretty much the public face for our group - a voice for Israel.
Kliman worked as a doctor in Alameda.