Sen. Paul Simon's home-state support appears to be slipping as the Illinois primary nears and he finds himself locked in a tight race with Jesse Jackson, according to the results of a newspaper poll to be published Monday. A Chicago Tribune poll of 500 Democrats likely to vote in Tuesday's primary shows Jackson with 32 percent of the support and Simon with 29 percent. But the poll, by Peter D. Hart and Associates has an error margin of plus or minus 5 percentage points, making the race a statistical dead heat. The latest poll, taken Friday and Saturday, updates one done earlier last week and published in Sunday's Tribune. That poll, with a similar sample and error margin, showed Simon holding 35 percent of the support to Jackson's 30 percent. ``I'm not saying every poll is inaccurate,'' Simon said while campaigning Sunday in Chicago's Chinatown. ``All I'm saying is if I get my message across to the people of Illinois, they're going to vote for me.'' Among other Democrats in the new poll, Massachusetts Gov. Michael Dukakis was third with 20 percent, Rep. Richard Gephardt of Missouri had 5 percent and Tennessee Sen. Albert Gore had 4 percent. The Tribune said 9 percent of the voters were undecided and 1 percent preferred none of the candidates. The newspaper did not update its Sunday poll of GOP voters, which found Vice Presient George Bush the overwhelming favorite among Illinois Repbulicans over rivals Kansas Sen. Bob Dole and former TV evangelist Pat Robertson. The new Tribune poll found Jackson's support strongest in Chicago, which represents nearly half of the state's likely Democratic primary voters. Simon did best in counties closer to his Southern Illinois home of Makanda and in the rest of Cook County outside Chicago. Support for the two was split among racial and sexual lines. Jackson was strongest among blacks and men, while Simon's support was heaviest among whites and women, the poll results show. Among occupations, blue-collar workers supported Jackson far more than other job classifications, while Simon's support was nearly even among all occupations.