A federal grand jury began taking testimony today about allegations of union corruption involving Secretary of Labor Raymond J. Donovan.

Sources said the first witness, Mario Montuoro, former secretary-treasurer of Local 29 of the Laborers Union, took the stand late this morning after he was promised immunity from prosecution for anything he might say, so long as it does not constitute perjury.

Montuoro had said earlier that he wanted immunity only for testifying that he pocketed $200 of an alleged $2,000 payoff in 1977 from an official of Donovan's company, Schiavone Construction of Secaucus, N.J.

Sources said that today Montuoro reportedly identified a photograph of Donovan as that of a man introduced to him at the luncheon where the payoff reportedly occurred. Montuoro has said the man was introduced to him as "a vice president of Schiavone."

Donovan has denounced Montuoro, whose union has worked for Schiavone Construction on a series of New York City subway projects, as "a damnable and contemptible liar." The labor secretary, who used to be executive vice president of Schiavone, has protested that he was never at the restaurant where the $2,000 allegedly changed hands, a place called Prudenti's in Long Island City.

According to Montuoro, a self-styled union reformer who was ousted from his Local 29 post in 1978, a Schiavone official he knew as "Joe DiCarlo" handed an envelope containing $2,000 in cash to Local 29 President Louis Sanzo as a "token of appreciation."

Today, however, sources said Montuoro was unable to identify DiCarlo from any of the pictures supplied by special prosecutor Leon Silverman and his aides.

Montuoro has said that Sanzo opened the envelope as the two of them drove away from the restaurant. He said Sanzo counted out 20 $100 bills and gave him two.

Sources in Washington said they believed Silverman is bent on conducting "a broad investigation" that covers other charges of Schiavone's bestowing favors on Local 29 officials in violation of federal labor law.

"I've heard that the scope of the inquiry will be broad and that it will take a while," said one source. "I'm still hearing that."

But so far Silverman appears to be concentrating almost exclusively on the alleged episode at Prudenti's. Montuoro said he first told federal authorities about it in late 1978 or early 1979 during an earlier investigation of corruption in mob-connected Local 29.

Today's session at the U.S. courthouse in Brooklyn contained what appeared to be some acrimonious notes, with Silverman and Montuoro shouting at each other in tones loud enough to be heard well outside the grand jury room.

There has been no indication of when other witnesses, such as Donovan or union president Sanzo, might be called. Sanzo's lawyer, Jeffrey Weisenfeld, said that both Sanzo and Local 29 secretary-treasurer Amadio Petito expect to be subpoenaed, "and when we get one, they'll go."

"Mr. Silverman appears to be going the perimeter route," Weisenfeld said the other day. "You start from the outside and work towards the center."

In any case, he said, "It is both my position and Mr. Sanzo's that he Silverman is not conducting a witch hunt. We may not always agree with him but we think he is running a fair and honest investigation."