CBS News Correspondent John Blackstone says they could be "ominous" clues.
Investigators collected the fragments as part of a search for any evidence that might link Phillip and Nancy Garrido to two other child abductions in the 1980s.
An earlier search of their next door neighbor's backyard also yielded a bone fragment that police say is likely human, but tests still must be completed.
The Garridos are already charged with kidnapping Jaycee Dugard in 1991 and holding her in a squalid encampment of tents and sheds at their Antioch home. Dugard was reunited with her family after the Garridos' Aug. 26 arrest. The Garridos have pleaded not guilty and are in jail.
Authorities returned to the couple's Antioch property this week after citing similarities between the Dugard kidnapping and the unsolved.
Hayward police Lt. Christine Orrey said investigators found a bone fragment in the backyard of the Garrido property on Wednesday and several bone fragments at a property next door where Phillip Garrido was once the caretaker.
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She said officials did not know if the fragments were human or animal, but they were being cautious because animal bones have been found on the properties before.
Investigators on Wednesday cleared brush, trash and other debris on both properties and tore down a carport and a shed on the Garrido property.
Once the sites have been cleared, search dogs will comb the yards and investigators will use high-tech equipment to search for soil disturbances that could indicate possible grave sites.
Probers "want to look under the walls and floors and they will tear the house down if necessary to discover its secrets," Blackstone reports.
Orrey said police haven't found anything that "breaks open our case," but they are still examining evidence.
Lt. Kurt Von Savoye said the same about the Dublin case.
"We found several items that we'd like to examine. At this point we are unable to determine if they are directly related or not," he said.
During their search, authorities found photographs they plan to give to Dugard that they believe are of her and her family. Investigators would not be more specific.
Police removed about three truckloads of trash and anticipate they will fill eight to 15 more. Police will examine all items before throwing any out, Orrey said.
Neither Hayward nor Dublin police have spoken to the Garridos or Dugard.
A note on the Web site for Nancy Garrido's lawyer, Gilbert Maines, said Maines was surprised to find the search under way, but he would not comment further.
An after-hours recording at the office of Phillip Garrido's defense lawyer, Susan Gellman, did not allow messages.