The D.C. Public Employee Relations Board yesterday ordered the city's police department to hold an election to determine which of two rival organizations should represent rank-and-file officers and sergeants in collective bargaining with the city.

The order results from a petition by the Fraternal Order of Police requesting the election to determine whether the International Brotherhood of Police Officers, the current bargaining organization, or the FOP should represent the police officers and sergeants.

FOP officials have maintained that the IBPO, which represents the department's 3,300 officers and sergeants, does not have the support of the officers they represent.

Nearly 1,100 officers have quit the IBPO since June to protest the latest contract it negotiated with the city, according to Gary Hankins, who heads the labor committee for the FOP. IBPO officials contend the number is more like 600 and many of them have returned in recent weeks.

Hankins said 1,680 officers signed the petition demanding the election and filed it with the Public Employee Relations Board last June 4.

However, the IBPO challenged the petition on several grounds, one of which was that the petition was filed after the IBPO had signed its new three-year contract with the city in June.

But the employe board ruled yesterday that the petition was timely since it had been initiated under the previous contract, which allowed petitions to be filed up to July 31.

Many of the police officers represented by the IBPO said they were upset with the new contract, which provides money bonuses in its first two years and a 7 to 9 percent pay increase in the third year.

Some officers who were not IBPO members, but were eligible to belong, were angry that the new contract required them to pay $5.50 every two weeks in union dues.

Hankins said he expects the election to be held in about a month.

Larry Melton, vice-president of IBPO Local 442, said, "The men have got a right to decide who they want to represent them."