The Justice Department has begun an investigation to determine whether an independent counsel should be appointed to pursue allegations of misconduct by Judge Douglas H. Ginsburg while he was a high-ranking government official, Justice Department sources said yesterday.

The sources said the threshold inquiry by the Justice Department's Public Integrity Section -- the first step in the formal process that could lead to appointment of an independent counsel -- will include examination of whether Ginsburg violated federal conflict-of-interest laws while he was an assistant attorney general in charge of the Antitrust Division from 1985 until last November.

Ginsburg withdrew from consideration for appointment to the Supreme Court last Saturday, nine days after being nominated, following his disclosure that he had smoked marijuana as recently as 1979 while a professor at Harvard Law School.

Before the marijuana disclosure, questions were raised about Ginsburg's handling at the Justice Department of several matters involving the cable television industry at the same time he had an investment of almost $140,000 in a Canadian cable television company that does business in the United States.

It could not be determined yesterday whether the public integrity inquiry is restricted to the cable issues, whether it is limited to conflict-of-interest allegations or whether it touches on Ginsburg's actions while a senior official at the Office of Management and Budget before becoming an assistant attorney general.

Sources said, however, that the inquiry does not involve Ginsburg's drug use, which does not appear to have violated federal laws, or any false statements related to the drug use.

Ginsburg did not respond to a request for comment. Justice Department spokesman John Russell refused to confirm or deny the existence of the inquiry.

On a questionnaire submitted to the Senate Judiciary Committee when he was nominated to the U.S. Court of Appeals here last year, Ginsburg said he was the "principal draftsman" of the department's brief in a Supreme Court case involving the First Amendment rights of cable operators.

Federal law makes it a crime for a government employe to participate "personally and substantially" in a matter in which he has a financial interest, unless the employe receives a "written determination

. . . that the interest is not so substantial as to be deemed likely to affect the integrity" of his services.

Although Ginsburg consulted informally with subordinates in the Antitrust Division about whether he should recuse himself from participation in the cable case, he did not seek the official clearance. Ginsburg's investment in Rogers Cablesystems Inc. was his only major investment other than real estate, according to his federal financial disclosure forms.

The 1978 Ethics in Government Act, which governs appointment of independent counsels, provides that the attorney general "shall conduct an investigation" whenever he

"receives information sufficient to constitute grounds to investigate" whether officials covered by the act have violated federal criminal laws.

As an assistant attorney general, Ginsburg would come under the act and be subject to investigation for up to two years after leaving the executive branch. Ginsburg became a federal judge one year ago.

The law provides for a 90-day preliminary investigation to determine whether to seek court appointment of a special counsel, after which the attorney general must either request the counsel or submit a report to a special three-judge panel explaining why no further action is necessary.

However, the Justice Department under the Reagan administration has been conducting "threshold inquiries" to determine whether a formal "preliminary investigation" is warranted.

The Ginsburg inquiry is at the earlier stage, the sources said. They cautioned that the existence of the inquiry does not in itself mean an independent counsel is likely to be appointed.