On the eve of the Democratic National Convention, the man Democrats will nominate as their presidential choice, Massachusetts Gov. Michael Dukakis, has slipped in Utah in his standing against Vice President George Bush, a new Deseret News/KSL-TV poll shows.

In a June 28-29 survey, pollster Dan Jones & Associates found that if the election were held today, 51 percent of Utah voters would vote for Bush, 36 percent favor Dukakis, 3 percent would vote for someone else and 11 percent didn't know for whom they would vote.The latest results are identical to those found by Jones in an April survey, 51-36 percent for Bush. In a May poll, Jones found that Dukakis had gained on Bush. Then, 47 percent said they would vote for Bush, 38 percent favored Dukakis.

When he visited Utah on June 12 to speak to the annual meeting of the U.S. Conference of Mayors, Dukakis said he won't concede any state to Bush, "even Utah."

Based on recent election results, Utah is the most Republican state in the nation. President Reagan carried the state with more than 70 percent of the vote in 1980 and 1984. Bush clearly won't do as well, but local GOP leaders hope Bush will run strong and thus help other Utah Republicans.

Unlike the Utah governor's race, where a number of Republicans say they'll vote for Democrat Ted Wilson, the presidential contest breaks out along party lines, Jones found. Only 11 percent of the Democrats said they plan to vote for Bush, while 11 percent of the Republicans say they favor Dukakis.

Reagan carried the West with large majorities. If Dukakis wants to win, he'll have to cut into that western Republican strength, political analysts say.

Last week, Dukakis picked Sen. Lloyd Bentsen of Texas as his vice presidential running mate, in part to help carry the West and South. But Bentsen is little known by Utahns. In a previous poll, only 1 percent of those questioned favored Bentsen as Dukakis' pick.

If the presidential election were held today and the candidates were Michael Dukakis, Democrat, and George Bush, Republican, for whom would you vote?

Definitely Dukakis 21 percent

Probably Dukakis 15 percent

Probably Bush 18 percent

Definitely Bush 33 percent

Other 3 percent

Don't know 11 percent

Sample size: 603; margin of error plus or minus 4 percent