Chicago Police Superintendent Richard J. Brzeczek, a target of criticism from mayoral nominee Harold Washington (D-Ill.), announced his resignation today, one week before the city's fiercely contested election.

Brzeczek, 40, who was appointed to the post by Democratic Mayor Jane M. Byrne and had appeared in Byrne television ads during her unsuccessful bid for renomination in the Democratic primary campaign in February, said he plans to join a downtown law firm.

He said he hoped his resignation, effective the day a new mayor is inaugurated, would remove his "personality" as an issue in Washington's contest with Republican Bernard E. Epton, but initial speculation was that it would fuel the controversy further. The resignation had been expected since Byrne's defeat in the three-way primary.

Washington criticized him during the campaign and said he would replace him with an officer from the Chicago force. He also said that, despite the city's budget problem, he hopes to expand the force by 1,000 patrolmen as quickly as possible, with emphasis on increased foot patrols.

On Monday, the Chicago Fraternal Order of Police released a poll showing that Epton was the choice of more than 92 percent of those officers who responded. FOP President John Dineen said Epton was named on 3,574 ballots and Washington on 256, with 34 expressing no preference.

Replies were received from slightly more than one-third of the city's police officers below the rank of sergeant.

Both candidates spent the evening prospecting for votes in Hispanic neighborhoods and along the city's affluent near-north lake front, two key enclaves of undecideds.

Epton, who like Washington pledged to search for a new police commissioner from within the department, appeared at a rally of Republican precinct captains in Chicago's Gold Coast of luxury high-rises and twitted his opponent over the most recent revelations about his failure to pay taxes.

"It would be so nice if we all paid our real estate taxes," he said in mock lament to an approving crowd. He was referring to a report today in The Chicago Sun-Times that property taxes totaling $2,200 were not paid for three years on a slum building owned by Washington, his brother and another man until they sold it in 1978.

The building deteriorated to the point that tenants were evicted by the city in 1977 for safety reasons.

Washington said that he and his co-owners were willed the building by his father and that rents were so low and uncertain that he could not afford to maintain the building or pay taxes.

The new owners agreed in the 1978 sales contract to pay the overdue 1975-77 taxes, Washington said.

Washington added that it was "ludicrous" to raise the nonpayment issue now, and referred all questions to his brother, who was not available for comment.

Washington also campaigned along the lake front, an area that he termed "vitally important" and where his support among professionals is thought to have eroded under the weight of the charges about his integrity.

He received a warm response from a group of elderly persons and at a fund-raiser of influential members of the business and professional communities.

He was greeted by frequent cheers from a crowd of about 650 people in a predominantly Hispanic neighborhood on the northwest side, but the appearance also drew about 30 hecklers identifying themselves as members of the Northwest Hispanic Democratic Coalition and wearing Epton buttons.

A member of the picket line, who asked not to be identified, said: "We're not prejudiced. We just have a nice clean neighborhood, and we don't know why they won't stay on the south and west sides."

Washington, who ran a distant third among the city's estimated 100,000 Hispanic voters in the Democratic primary, was endorsed today by a key Spanish-language newspaper and television station.

Epton visited Wrigley Field this afternoon to demonstrate his loyalty to daytime baseball at the only major-league stadium without lights and to brag of other stands he has taken for preservation of the urban environment.

Chicago Cubs fans gave him a friendly reception as everyone suffered through a chilling rain that eventually forced postponement of the Opening Day game with Montreal.

Meanwhile, the Chicago Board of Elections announced that voter registration has increased by 31,536 persons since the primary to a total of 1,625,786.

Officials said that some of the largest increases are in black wards, but that whites' overall registration edge probably was not decreased.

Estimates are that blacks comprise about 40 percent of the voting population.