An arbitrator ruled yesterday that the Metropolitan Police Department improperly transferred a sergeant in retribution for reporting alleged irregularities in the compilation of crime statistics and ordered that he be restored to his former job with all back pay and allowances.

The decision by arbitrator Jacob Seidenberg in behalf of Sgt. Raymond Dyer caps a controversy that began more than a year ago. In September 1981, the former 6th Police District detective was abruptly tranferred to scooter patrol following his complaints to union officials that crimes occurring in the 6th District systematically were being reported in less serious categories--for example, downgraded from felonies to misdemeanors--to make it appear that the area had fewer serious crimes.

Gary Hankins, chairman of the Fraternal Order of Police's bargaining committee, hailed yesterday's ruling, saying it "confirmed the union and Ray Dyer's position down the line." Hankins said that Dyer, in "reporting something that was wrong . . . became a victim of a conspiracy of attempts to repress it."

Hankins said the 31-page report released yesterday stated that key figures in the department knew Dyer had complained to union officials at the time he was transferred. Hankins said the report listed as among those officials Assistant Chief Marty Tapscott; Deputy Chief Isaac Fulwood, commander of the 6th District; Capt. Larry Soulsby and Sgt. Zelford Platt, Dyer's immediate supervisor.

Reached by telephone last night, Tapscott declined to comment on the decision. Tapscott, who said he had not yet seen a copy of yesterday's report, said that since the controversy over crime classification arose, "minor corrections" have been made to an otherwise "sound" system. He declined to elaborate on those changes.

Fulwood, who commands the 6th District that includes Capitol Hill, said last night that he had not seen the report. "Sgt. Dyer has been doing a good job in the job he's in," Fulwood said, "and if he goes back to the detectives' office I expect he'll do a good job there."

Dyer's complaints were investigated by Deputy Chief Roland W. Perry, who said that some officers were told to downgrade reports and that Dyer was transferred because of his opposition to the practice.

But Tapscott, Perry's supervisor, reviewed Perry's findings, conducted his own investigation, and overturned Perry's recommendations. Chief Maurice T. Turner accepted Tapscott's recommendations.