Labor relations involving the District of Columbia and its employe unions are becoming more turbulent.

Coinciding with the breakdown of bargaining between the city and its unionized firefighters, the D.C. Public Employe Relations Board (PERB) has issued a sternly worded order declaring that the police officers' union is dragging its heels in holding an election in which officers could choose between it and a rival group.

PERB said Local 442 of the International Brotherhood of Police Officers "has refused to proceed with the implementation of the Oct. 9 order" issued by PERB requiring a representation election, "and has further advised the board that . . . it will continue on this course."

PERB told the union to meet within three days with representatives of the rival group, the Fraternal Order of Police, to make arrangements for an election. It ordered both sides to report progress by next Thursday.

"The real issue . . . is whether the . . . procedures established in the D.C. Comprehensive Merit Personnel Act are to be respected," PERB declared in criticizing the union.

Union spokesmen could not be reached for comment. Gary Hankins, spokesman for the fraternal order, said a meeting with the union has been set for Monday afternoon.

The dispute began early this year when the fraternal order began proceedings to force a representation election in its bid to replace the union. The controversy was heightened in June when the union signed a three-year contract with the city that, among other provisions, provided bonuses in lieu of salary increases in its first two years.

On Wednesday, the D.C. firefighters' union declared its negotiations with the city to be at an impasse, forcing the issue into mediation.