The Chicago Police Department, one of the nation's most politicized and racially divided big city forces, has become deeply involved--mostly off duty--in the bitter Chicago mayoral campaign.

The white majority is heavily behind Republican Bernard E. Epton and blacks are supporting Rep. Harold Washington (D-Ill.).

Epton buttons adorn the jackets of white policemen as they travel to and from their shifts. Black policemen in private conversations make no secret of their hopes that Washington will succeed Mayor Jane M. Byrne in Tuesday's voting.

There have been no reported incidents of racial conflict in the 16,000-member police force, but feelings are running high.

In general, the white police officers, who make up 76 percent of the force, deny that their support for Epton is racially motivated.

"This is not a racial thing," one white lieutenant said. "I worked with blacks for years and I'm no racist." He said he is backing Epton and doesn't mind saying so--"just don't use my name."

A white patrolman, asked about an Epton button he was wearing home, replied: "This is my right. Who says I can't wear it? I'm not on duty, and what I do when I'm off duty is my business."

Black police officers, whose numbers have grown to 24 percent of the force from 10 percent since 1970, see it differently.

"White officers have always denied there's racial animosity against blacks, but now they're acting it out," said Renault Robinson, founder of the Afro-American Police Association and an adviser to Washington. "Now you've got white officers on and off duty challenging black voters."

Ten white detectives on off-duty hours have challenged the registrations of 2,500 voters, mostly in predominantly black wards in the southwest side. The Board of Elections Commission has ruled that about half the challenges by the detectives are valid. There may be more disqualified voters as a result of the police challenges.

"The police seem to see themselves as having an important political role and have been making maximum use of it," The Chicago Tribune said in an editorial Thursday.

The paper blamed police superintendent Richard Brzeczek, who announced his resignation this week after three years in office. Brzeczek was the center of controversy during the February Democratic primary campaign, when he made a TV commercial backing Byrne and, after the mayor lost, vowing to resign rather than work for Washington.

Meanwhile, the Fraternal Order of Police (FOP), the heavily white official bargaining agent for patrol- and detective-grade officers, counts seven current or former policemen among the City Council's 50 aldermen, all Democrats. Three of the seven are black. Eight current or former police officers ran for City Council in the February primary, and two, one black and one white, are in separate runoff contests to be decided Tuesday.

The FOP polled its 11,000 members, and to no one's surprise reported that 92.5 percent of those responding backed Epton. During the primary an FOP poll showed heavy support for Byrne.

Washington dismissed the recent poll, saying, "It depends on who does the counting." He has been endorsed by the Latin American Police Association, which has 250 members.

FOP Treasurer William Nolan said members are upset over Washington's calls for a civilian review board of the police force and changes he has proposed in investment policies of the $500 million police retirement fund.

In a related development, the city has agreed in federal court to substantially reduce the 200,000 disorderly conduct arrest and jailings racked up annually by Chicago police.

The American Civil Liberties Union charged in a lawsuit that police used spurious disorderly-conduct arrests to sweep the streets of black neighborhoods.

ACLU executive director Jay Miller said "90 percent" of the estimated 500,000 such arrests over the past three years involved black or Hispanic males.