Four major labor unions are spending considerable time, energy and money in a hard-fought and bitter campaign to win the votes of 5,800 D.C. police and prison employes -- a massive effort that will result in no gain in total union membership because the city workers already are unionized.

Three-way election campaigns at the Metropolitan Police Department and the Department of Corrections were sparked by substantial dissatisfaction with the current unions among public safety employes, who believe the unions should push the D.C. government harder for improvements in pay, benefits and often-dangerous working conditions.

But the campaigns also reflect a growing problem within organized labor: Many unions are depleting their scarce resources by "raiding" each other's jurisdiction and fighting off such challenges, rather than reaching out to organize the unorganized members of the work force.

"It is a waste of resources . . . . There is a lot of concern about this kind of internecine warfare," said Charles McDonald, the assistant director of organizing for the 13 million-member AFL-CIO.

Such battles are increasingly common in the public sector, McDonald said, because unions find it easier to win these elections than those in the private sector, where strong employer opposition often helps defeat union drives.

Unions win roughly 65 percent of government employe elections and represent more than one-third of all government workers, but labor wins only about 45 percent of private sector elections and represents less than one-fifth of the employes, according to data compiled by the AFL-CIO and the National Labor Relations Board.

The AFL-CIO, which consists of 96 unions, bans any member union from attempting to raid another's turf. But in the District, only one of the four unions vying for city workers belongs to the federation, so the ban does not apply.

The corrections department's 2,300 officers and civilian workers will vote Tuesday in a contest that includes the American Federation of Government Employees (AFL-CIO), which has represented prison workers for 30 years, and two challengers -- the International Brotherhood of Teamsters and the Fraternal Order of Police.

The police department's 3,500 officers and civilians are voting by mail ballots, which will be opened Friday, in a contest that includes the Fraternal Order of Police, the incumbent union, and two challengers -- the AFGE and the National Association of Government Employees/International Brotherhood of Police Officers.

Mayor Marion Barry sought to prevent the elections, because the city believes that neither the FOP nor the AFGE should be allowed to represent both police and prison employes. The city said such a situation would cause problems if police were called in to replace striking prison guards, as they were in a 1981 strike.

The Public Employee Relations Board, however, overruled the protest and ordered this week's elections.

The four unions have competed primarily through a barrage of mailings and leaflets, each touting its ability to fight effectively for better conditions; they also attack their competitors for ineffectiveness, lack of experience or requiring heavy dues that often are paid to national headquarters rather than being contributed to local efforts.

City labor relations officials said the months-long campaigns have been marked by mudslinging, apparent "dirty tricks" and harsh rhetoric. Several union leaders already have indicated that if they lose, they will file legal challenges.

"We're having a very bitter campaign," said an official from the Public Employee Relations Board, which oversees labor-management relations among city employes. " . . . I'm sure there will be lots of lawsuits" contesting the elections.

At D.C. Jail and Lorton Reformatory, severe crowding, inadequate equipment and dangerous working conditions have been perennial complaints of corrections officers. Inside the prisons, corrections officers complain bitterly about what they see as a lack of respect, and about their pay, which starts at $15,000 and generally lags $5,000 to $6,000 behind police and firefighters.

Dissatisfaction aimed at AFGE Local 1550 grew so intense last year that more than half the corrections employes petitioned the Public Employee Relations Board seeking to quit the AFGE and join the FOP.

"We had so many grievances about so many things we asked them to address, but they didn't move," said Larry Bryant, a nine-year veteran who broke with the AFGE to organize on behalf of the FOP.

The AFGE's problems grew so severe that the union's Washington headquarters, citing "mismanagement" and "undemocratic practices" by Local 1550, took over the local union and installed temporary officers. Now, the AFGE, acknowledging its past "serious lack of leadership," said that its 30-year history of dealing with D.C. officials and Congress gives it the experience needed to bring about prison reform.

"We have won significant improvements in your pay, working conditions and benefits. Veteran officers will recall the many battles we've waged with city government to win respect for you and your coworkers," AFGE President Kenneth Blaylock said in a recent letter.

" . . . We are capable of mistakes," the letter continued. "We are also capable of taking steps to remedy those mistakes" by beefing up union staff and lobbying efforts.

Both the FOP and the Teamsters Local 246, however, argue that the AFGE has been too easy on city government. The 1.9 million-member Teamsters, the nation's richest union, cites its $176 million net assets and its large staff as an example of its clout.

Teamster spokesman Peter A. Bonavita, a former Fairfax County police officer, said the Teamsters can be tougher bargainers because the union uses more "outside" staff. He said FOP and AFGE local officials, because they are police and corrections employes, often are afraid to take stands against city management because their jobs and promotions can be jeopardized.

In the police election, the charges of "dirty tricks" include allegations by the FOP and the AFGE's Alliance of Metropolitan Police Officers that the third contestant, the National Association of Government Employees/International Brotherhood of Police Officers, somehow gained access to the home addresses of some police officers and sent them union mailings.

Under federal law, the home addresses and telephone numbers of police officers are confidential.

In a Jan. 11 letter to AFGE national organizer Roscoe Grant, Mark Levitt of the D.C. Office of Labor Relations wrote, "We confronted NAGE/IBPO officials about the matter which then led us to believe that the data was somehow obtained through the D.C. Police and Fire Retirement Board."

Donald H. Weinberg, head of the labor relations office, said the matter will be "dealt with internally within the police department . . . . Certainly all parties should have the same opportunities."

Susanne Poole, vice president of NAGE/IBPO, said no addresses were obtained surreptitiously. She said the union, which formerly represented D.C. police, "knew a lot of police officers" and drew other addresses from sheets signed by officers when they petitioned for the election last year.

Controversy also arose over a bogus IRS tax form sent anonymously to some officers, purporting to show that Gary Hankins, chairman of the FOP's labor committee, received more than $77,000 in income from the organization last year. "This goes beyond the bounds of campaign practices," Hankins said. "It is a complete fraud."

An inspector for the U.S. Postal Service said the matter has been turned over to the U.S. attorney's office. "It's not right," he said, "but I'm not sure there is a violation" of law.

Inspector Bobby J. Wallace, head of D.C. police labor relations, said that depending on the outcome of the investigation, the FOP may have grounds for contesting the outcome of the election to the Public Employee Relations Board.

Among the police, much debate has centered on whether unionized officers, whose base pay ranges from about $19,000 to $27,000, would be better served by a large national labor organization or a more decentralized union. The AFGE and the NAGE each have more than 200,000 members, while the FOP is smaller and actually is a fraternal group, which has individual union subsidiaries and a headquarters operation that is less costly to run.

The FOP has been criticized for being largely a "social" organization with little experience in contract negotiation. Hankins said the union has staked out tough bargaining positions and "is the only [contestant] where the power, authority and finances remain concentrated at the local level." FOP members pay only $2 in national dues, compared with substantially higher amounts for others.

Harry Breens, national executive secretary of NAGE/IBPO, said his group, the largest police union in the country, is better qualified to "protect the officers' benefits on all job-related matters."

J.C. Stamps, president of AFGE's police contingent, said the FOP offers officers "a social atmosphere . . . but they're not good as a labor representative." Stamps said his competing group is made up of officers with an average of 16 years on the force, "and we should know by this time what our officers need, want and should have."