The bitter Chicago mayoral battle is going into its final week with strategists on both sides agreed that underdog Republican Bernard E. Epton has moved into a position where he is almost an even-money bet to upset Rep. Harold Washington (Ill.), the Democratic nominee.

Ironically, though the campaign for the April 12 election has been dominated by the racial polarization over Washington's bid to become the first black to run this city, the final week's effort on both sides is focused on the relative handful of voters who are trying to see beyond the race issue that has brought national and international attention to this fight.

Both Epton and Washington put on new television commercials this weekend aimed at the so-called "lakefront liberals," a small but affluent and politically active slice of Chicago's citizenry who are telling pollsters on both sides that they are torn by doubts about both contenders. The two former legislators will spend much of their remaining campaign time with these hitherto neglected voters.

Washington, thrown on the defensive the last two weeks by a series of Epton attacks on his integrity, is firing back with tough new ads depicting Epton as a "puppet" for Ronald Reagan and the Republican Party, which Washington says has ordered Epton to run what he calls a racist campaign. Washington supporters also hit Epton today for allegedly building his law practice from insurance business while serving as head of the legislature's insurance committee.

Epton is responding with positive, issue-oriented ads, aimed at strengthening his image with the only constituency in the city that may be more interested at this point in the policies the new mayor will follow than the color of his skin.

The seven lakefront wards (of the city's 50) have a reputation for political independence. They are dominated by liberal Democrats who sometimes cross party lines to support reform-minded Republicans. Many of the residents are Jewish, and Epton, a Jewish, liberal Republican who represented one of the lakefront wards for 14 years in the legislature, is, in the words of one Washington strategist, "the best kind of candidate the Republicans could have for the lakefront."

All told, the seven wards cast fewer than 200,000 votes. But the polarization of the rest of the city makes their votes crucial. Both campaigns took fresh polls this week, and, while the exact figures remained secret, the results on both sides pointed to a close race.

"My guess is that it will be decided by 30,000 to 50,000 votes either way," said John Deardourff, the Epton campaign consultant whose TV ads, urging Chicagoans to vote Republican "before it's too late," have fueled controversy. "The fact is, this is a very close race, period," echoed Washington campaign manager Al Raby.

Both camps believe the emotional intensity in black and white neighborhoods will translate into a vote than may reach or top 1.3 million, better than an 80 percent turnout. Both sides expect Washington to receive about 500,000 black votes, 100,000 more than he won in the primary. Both see at least 500,000 white ethnic votes (almost all nominal Democrats) for Epton. "The northwest side and the southwest side are gone," said one Washington manager, referring to the Polish, Irish, Italian, German, Greek and Slavic neighborhoods.

One battleground is the Puerto Rican and Hispanic community, where Washington ran poorly in his primary contest with Mayor Jane M. Byrne and Cook County State's Attorney Richard M. Daley, and was campaigning today with New Mexico Gov. Toney Anaya (D).

But the more important front for the final week is the lakefront. Whereas "95 percent of the committed vote, on both sides, is based on the race of the candidates," according to one Republican strategist, the "lakefront liberals" can be appealed to largely on the basis of issues.

"We have gone about as far as we can in our attacks" on Washington, said Deardourff, referring to the series of ads focusing on Washington's conviction and jail sentence for nonpayment of income taxes and his temporary disbarment for misappropriating clients' funds.

While Democrats contend that the tagline on those ads is a barely disguised racist appeal, Deardourff and Epton, both liberals on racial and social issues, deny it. "Our message is not that he's black and therefore a threat," Deardourff said. "Our message is that he's a crook and therefore a threat."

In any case, he said, "The last 10 days, we will be considerably more positive in our appeal. The target is the non-black, non-ethnic whites, many of them younger people, who won't vote purely on the basis of race. We want to show them Bernie is a solid, responsible, progressive guy who will govern well for the whole city." The vehicle is a series of deliberately unemotional "Epton-on-the-issues" ads, with the slight, bearded candidate talking about taxes, transit, public safety, economic development and other bread-and-butter concerns.

Democrats concede that Epton has targeted his message correctly. "The lakefront is a very issue-oriented constituency," said Joanne Alter, a liberal Democratic activist and sanitation commissioner who supports Washington. "Our voters are the kind who read 52-page issue papers." When Washington issued such a collection this week, Alter said her reaction was, "Thank God, we finally got an issues book."

But Washington is not leaving it to the issues books. He is launching a belated TV campaign, showing an Epton-like marionette with its strings being pulled by Reagan and the GOP. "If you're thinking about voting for Epton, think about who is pulling his strings," the announcer says.

In tandem with the ads, the Washington camp is doing a targeted direct-mail campaign into the lakefront wards and is stepping up its effort to fuel doubts about Epton's finances and medical history.

At a press conference today sponsored by the Washington campaign, the Illinois Public Action Council, a coalition of citizens' groups, released a report charging that Epton's law firm received more than $1.3 million in fees from insurance clients between 1978 and 1982, while he was ranking Republican on the state House insurance committee and chairman of the state insurance laws study commission. The report charged that Epton "was enmeshed in conflicts of interest so pervasive that he in fact sold his seat in the House to the state's insurance industry."

Epton replied, "I, more than any other legislator, have introduced legislation to protect Illinois consumers from abuses by the insurance industry."

It was reported earlier that Epton had been hospitalized twice for psychiatric tests. He said the hospitalizations were for unexplained migraine headaches and abdominal pains that turned out to have been caused by ulcers.

Washington said Friday night that he would meet Epton in another debate, as the Republican has been demanding, but only if Epton released all his medical and psychiatric records and his income tax returns.

Some in the Washington campaign concede that the counterattack is so late and so negative that it may seem a desperation move. In a city where the Democratic mayoral nomination has been tantamount to election for 52 years, many politicians of both parties criticize Washington for allowing himself to get mousetrapped by the heretofore unknown Epton.

"Washington could have put this election away in the first 72 hours after the primary," Deardourff said. "He's run a very sloppy campaign."

That judgment is echoed privately by many white Democratic politicians, who say that Washington's unwillingness or inability to reach out to those who supported Byrne and Daley in the primary (which Washington won with a largely black 36 percent plurality) created the opening for Epton. Democratic pollster Patrick Caddell, who polled for Washington in the February primary, said he warned his candidate immediately that at best he could not expect to win more than "52 or 53 percent of the vote" against Epton.

A contributing factor, many say, was the belief by Washington and his aides that after so many years in which blacks had loyally supported white Democratic candidates, Washington "should not have to beg" white Democratic leaders to support him.

The result is that this election goes into its final week with the Republican in striking distance of victory and the momentum seemingly in his direction. As a worried Al Raby said Friday night, "We need to go to more of the places that symbolize that our campaign is for the whole city."