Republican Gov. James R. Thompson barely avoided a political calamity yesterday when the State Board of Elections ruled that a Thompson-sponsored advisory referendum urging a ceiling on property taxes may be submitted to voters.

But the ruling did little to quiet calls for criminal investigations of charges that thousands of signatures were forged on petitions circulated by Thompson workers in a frantic, last-minute campaign to put the proposition on the Nov. 7 ballot.

The board, made up of four Republicans and four Democrats, found 15,608 forged or otherwise invalid signatures on the petitions, but it ruled 591,802 other signatures were valid. That was just 2,387 - or four-tenths of 1 percent - more than necessary.

The relieved governor, who has made no secret of his presidential aspirations, told reporters after the board's unanimous ruling that he would ask the state director of law enforcement. Tyrone C. Fahner, to investigate the allegations. Although Fahner is a Thompson appointee, the governor said he believes Fahner's "integrity is widely enough accepted" that there would be public confidence in the inquiry.

"I don't have any knowledge of any people in the Thompson campaign committing any criminal act," Thompson said, "and I would be shocked to find that there were any."

Defending the challenged petitions, he added, "I think it's fair to say that the charges of wholesale forgery have not proved to be the case."

In some instances, he said, signatures that were labeled as forgeries were "commonplace in the Illinois petition business" - such as husbands signing their wives' names.

Challengers of the signatures - Democratic legislators, the Illinois Education Association, Independent Voters of Illinois and other groups - said they will decide next week whether to appeal the Board of Elections' ruling to the courts.

Among those calling for criminal investigations in the president of the Illinois Bar Association, Lloyd J. Tyler Jr., who is angry because his signature and his wife's and son's signatures were forged on one petition.

During the Board of Elections investigation, Vicki Sands, executive secretary to Lt. Gov. Dave O'Neal vowed to take the Fifth Amendment if forced to testify about petitions she had notarized. Thompson then withdrew petitions containing 8,600 signatures on petitions she notarized.

The proposition states, "Shall legislation be enacted and the Illinois Constitution be amended to impose ceilings on taxes and spending by the State of Illinois, units of local government, and school districts?"

Opponents contend the referendum is meaningless because it is merely advisory and would have no legal force. But Thompson made the proposal the centerpiece of his campaign for relection to a second term in November.