The Justice Department yesterday dropped its conspiracy investigation of Sen. Howard W. Cannon (D-Nev.), chairman of the Senate Commerce Committee, and turned the cased over to the Senate Ethics Committee for further review.

As part of the lengthy investigation, sources said, prosecutors gave grants of immunity to Teamsters union President Frank Fitzsimmons and Allen Glick, who has been linked to organized crime, for their testimony. Glick has been the subject of numerous federal investigations of organized crime ties to the teamsters and Nevada gambling casinos.

It was disclosed in February that a federal grand jury in Chicago was investigating whether Cannon had agreed to derail a trucking deregulation bill in return for a chance to bid on some Teamsters union land in Las Vegas that he and his neighbors wanted to save from high-rise development. But the bid was rejected, the deregulation bill was passed, and now the prosecutors have dropped the inquiry.

Cannon acknowledged at the time that he had discussed the land and an alternative form of deregulation in his Las Vegas office in January 1979 with Allen Dorfman, a former Teamsters union pension fund consultant who was convicted of defrauding the fund in 1973, and Teamster officials. But he denied any impropriety.

Sources familiar with the case said that an FBI wiretap of Dorfman picked up a telephone converstaion with the senator in mid-1979, the contents of which have not been disclosed, and calls between Dorfman and Teamsters official Roy Williams in Kansas City in which the two men bragged that Cannon had put the trucking bill on the back burner. These helped touch off the Justice Department investigation.

Cannon did take jurisdiction of the bill in his committee in March 1979, after Sen. Edward M. Kennedy (D-Mass.) had announced plans to hold hearings on it in his Judiciary Committee. The bill was passed and signed into law in July.

In a statement yesterday, Cannon said, "I am pleased that my conduct as a U.S. senator and as a neighbor to my friends has been vindicated by the conclusion of the investigation."

The 68-year-old senator said he had cooperated with the investigators by providing sworn testimony as well as documents to the grand jury. His attorney, John Dowd, added that the evidence in the case showed that Cannon led the fight for trucking deregulation which the Teamsters opposed.

Philip B. Heymann, head of the Justice Department's criminal Division, sent word yesterday to Sen. Howell Heflin (D-Ala.), chairman of the Ethics Committee, explaining the decision not to seek an indictment. Heflin had returned to Alabama yesterday and was not available to comment on what the committee plans to do about the case.

A spokesman for Sen. Malcolm Wallop (R-Wyo.), who will become chairman of the committee in January, said he had not heard anything from Heymann.

The investigation of Cannon grew out of one on Dorfman known by its FBI code name "Pendorf." When word of the inquiry leaked to the press in February, Attorney General Benjamin R. Civiletti ordered that it be included in a leak investigation along with unauthorized disclosures about the undercover Abscam investigation of other members of Congress. No final decision has been made about disciplining Justice or FBI employes in any of the leak investigations.