The Democratic national chairman yesterday asked the Justice Department for a formal investigation of alleged voter intimidation in last Tuesday's New Jersey gubernatorial election.

DNC Chairman Charles T. Manatt's request came as the counting continued in the closest election contest the state has seen in a century. Late yesterday afternoon, former Assembly speaker Thomas H. Kean, a Republican, was leading Rep. James J. Florio, a Democrat, by 1,795 votes--down from a 1,947-vote margin when the re-checks were halted for the weekend.

The focus of Manatt's request was the role of a "ballot-security task force," financed by the Republican National Committee and the New Jersey Republican Committee. Members of the task force--some of them armed, off-duty policemen-- were seen at polling places in several cities, with posters warning, "It is a crime to falsify a ballot or to violate election laws."

Manatt asked the Justice Department to determine if the presence of the security patrols, largely in black precincts, was part of "a conspiracy. . . to intimidate, threaten or coerce" voters.

A Justice Department spokesman said the letter had been referred to the civil rights division and said it will "move as expeditiously as possible" to determine if there is a federal jurisdiction.

Sen. Bill Bradley (D-N.J.) pointed out to reporters yesterday that the intimidation charge would require an affidavit or testimony from an individual who was dissuaded from voting by the presence of the security men. Any such testimony, he said, would be subject to cross-examination and the whole process might cloud the determination of a winner.

Meantime, state officials struggled to get an accurate tally of the votes, with substantial changes reported during the day in several counties.