A private Washington consulting firm has been hired by the Labor Department - at $50 an hour - to negotiate a contract between the department and an employee union representing many of its headquarters workers.

The unusual agreement is part of the long-running, generally unsuccessful effort of the department - which sets Labor rules for most private employers and unions - to come to terms with Local 12 of the American Federation of Government Employees.

Labor and the AFGE have been at odds for months in negotiations for a new contract that expired long ago. At one point the parties went to the Federal Services Impasses Panel - the court of last resort in internal government labor disputes - but the panel, in effect, told them to try again.

The firm that will do the bargaining for Labor and set up a labor education program for managers is Ruttenberg, Friedman, Kilgallon, Gutchess and Associates. Stanley Ruttenberg was a top Labor official during the Kennedy-Johnson administrations (he took Daniel Patrick Moynihan's place). The firm - which usually represents labor groups - helped the Professional Air Traffic Controllers Organization in a recent - and successful for the union - grade reclassification dispute with the Civil Service Commission.

Labor has been unable to reach final agreement with the AFGE. Each side blames the other for being unwilling to talk, or unwilling to discuss reasonable concessions since bargaining began in early 1975.

Last summer, just before a planned Labor Department Labor Day gala at the Kennedy Center, the union threatened to embarrass then Secretary William J. Usery whn he spoke by flooding the area with placards calling him antilabor. The union called off the demonstration after Labor, at the last minute, agreed to a union demand to restrict severely hiring and promotion for most headquarters jobs.

That plan bars many Labor Department workers, all other federal employees and all outside job-seekers from many headquarters positions. It limits the candidates for promotion, or to nonentry level jobs to employees in the bargaining unit represented by the AFGE local. That local, meantime, has had internal problems of its own.

Acting on the complaints of several AFGE union members at the department, The Civil Service Commission determined that there had been numerous "irregularities" in the June, 1975, election that returned local president Russell Binion to power. Binion is a Grade 14 ($28,725 to $37,347) employee in headquarters.

A CSC judge has recommended that the department order a rerun of the 1975 election. If that action is approoved by CSC's vice chairwoman, the department and the union - barring successful appeals - would have to restage an election that took place more than 21 months ago.

The decision to bring in an outside firm to do what other federal agencies do routinely - bargain with employee groups - is technically unrelated to the election rerun. But other problems the department and its union have been having are a major factor in the decision to bring paid outsiders into the deliberations.

During the closing days of the Ford administration, Labor called in an outside panel of three arbitrators to study the labor-management program of the department.

They concluded, in effect, that the program wasn't working very well, that the workers and management should spend more time bargaining in good faith and that the in-house procedures for handling labor disputes should be revamped.

The department, which is a trifle red-faced about labor unrest within its own building, will finance the new consultant study out of funds from Congress. Congress gets the money from you. All are hoping not too many $50, 60-minute sessions are necessary to resolve the dispute.

Alan K. Campbell apparently will be President Carter's choice to head the Civil Service Commission. The 53-year-old dean of University of Texas' public administration school is well known around Washington and in the public service community. On March 15 this column reported that Campbell was a good bet to get the top CSC job. White House officials now say he will, and that the appointment will be announced officially within a week.

L. Lawrence Schultz is the March 30 luncheon speaker at the Society of Labor Relations Professionals meeting at the Empress Restaurant. Schultz is director of the arbitration section of the Federal Mediation and Conciliation Service. Call 525-1914 for reservations.