The district attorney for Los Angeles County, John K. Van de Kamp, yesterday said that his office has begun a criminal investigation into Columbia Pictures studio president David Begelman's alleged embezzlement of more than $60,000 from the company.

Columbia Pictures had declined to press charges against Begelman, who recently was reinstated as head of the studio after an investigation. And the District Attorney's Office earlier had responded to inquiries by saying it would not take up the matter without a complainant.

"We are now looking into the case," Los Angeles D.A. spokeswoman Carole Welch said yesterday. "Rather than rely on independent reports from the police departments (of Burbank and Beverly Hills), we're looking into it."

Begelman was suspended as studio chief at the beginning of October after Columbia Pictures Industries Inc., the parent company, said it was looking into certain unauthorized transactions he conducted.

On Dec. 19, the company said Begelman was returning as studio chief, but tht he would lose his titles as director and chief executive vice president of the parent company, whose largest unnit is the studio.

The company disclosed the investigation had discovered "that in a number of separate and unrelated transactions from January 1975 to May 1977, Mr. Begelman obtained through improper means corporate funds in the amount of $61,008 for his personal benefit."

But the statement added that Begelman was undergoing psychiatric treatment and said that "the emotional problems which prompted these acts, coupled with ongoing therapy, will not impair his continuing effectiveness as an executive." Begelman has paid back the $61,008 plus interest, and is due to pay back $23,200 in challenged expense account items.

The police departments of Burbank and Beverly Hills had conducted preliminary investigations after actor Cliff Robertson last year turned over information indicating that Begelman had forged Robertson's endorsement on a $10,000 check and then cashed it.

Robertson, who had not worked for Columbia the previous year, said he uncovered the situation after he received an Internal Revenue Service tax form from Columbia Studios indicating a $10,000 payment and had tried to clear up the matter.

However, a juridictional dispute between the Burbank and Beverly Hills police departments, both in Los Angeles County, apparently allowed the case to fall between the cracks.

The Beverly Hills police said the case belonged to the Burbank police, because that's where the Columbia studio is located, and the Burbank police said the Beverly Hills police had jurisdiction because that's where the check was cashed.

A frustrated Robertson finally informed the FBI about the matter last fall.

"We have asked investigators of both police departments for their reports now," the D.A. spokeswoman said.

Besides the $10,000 Robertson check, sources say Begelman also forged a $5,000 check using the name of director Martin Ritt, and a $25,000 check using the name of an undisclosed person who apparently is not a member of the movie industry. Sources say Begelman also opened phony bank accounts in the name of third parties and had Columbia deposit funds in these accounts, which he somehow was able to draw on.