The ruling also sets up a high-stakes battle between Calpers and other creditors, including Wall Street bondholders and insurers, over how they will be treated in the bankruptcy.
The preliminary ruling follows a similar judgment for the city of Stockton, California, which was found eligible for bankruptcy protection in April.
Judge Jury said after her preliminary ruling that she would hear arguments from the parties, including Calpers, but it is considered unlikely that the judge will change her mind after having made clear her thinking.
"I don't think anyone in this courtroom seriously thought the city was anything but insolvent," Jury said. A city must be insolvent and have proof to have negotiated in good faith with creditors to be eligible for Chapter 9 municipal bankruptcy.
In an unusual move, Jury did not hold a full trial to determine eligibility. Instead, because of long delays in the case, she invited the city to apply for summary judgment to expedite the proceedings.
(Read more: Detroit bankruptcy case could bring unwanted change in munis)
San Bernardino filed for Chapter 9 bankruptcy protection last August, citing a $46 million deficit and arguing that it had effectively run out of cash to meet its daily obligations. At the time, the mayor said the city was overwhelmed by pension debt.
Calpers argues that it should not be treated like other creditors and must be paid in full because of California state law. Bondholders argue that federal bankruptcy law trumps state statutes and say Calpers should be forced to fight with other creditors over how much they are paid under an exit plan.
The issue, which is also likely to be central in the bankruptcy cases of Stockton and Detroit, could reach the U.S. Supreme Court.
In an unprecedented move, San Bernardino stopped paying its $1.2 million bimonthly employer payments to Calpers for a year after declaring bankruptcy, the first California city to halt payments to America's biggest public pension system.
It resumed paying Calpers last month but continues to renege on payments to other creditors, including holders of $50 million in pension obligation bonds.
The judge said the one creditor who wanted her to dismiss the bankruptcy was Calpers. But she said: "If Calpers gets all the money they want, under what they say is their statutory right, who isn't going to get paid? All the employees? How is that going to help Calpers?"
The case is In re San Bernardino, 12-bk-28006, U.S. Bankruptcy Court, Central District of California (Riverside).