Cleveland — Poor Ohio. In 1976, its legislature moved the presidential primary from May to June in an effort to become national powerbrokers if the race went to the wire.
After two dull primaries, the legislature last year switched the date back to May, hoping to boost favorite-son John Glenn's presidential chances with stronger voter interest.
But Mr. Glenn dropped out of the race. And Ohio Secretary of State Sherrod Brown sees little voter enthusiasm for Tuesday's contest.
Late last week Mr. Brown predicted that only 42 percent of Ohio's 5,892,814 registered voters will vote in the primary, which will send 175 Democratic and 89 Republican delegates to their respective conventions. That level is lower than in June 1980, when the renomination of President Jimmy Carter was nearly a foregone conclusion. Though the state's Democrats supported Mr. Carter that June , they deserted him in November.
''A lot of people thought that if we moved (the primary) a month up, we'd get in on some of the action,'' said David Shutt, communications director for Brown. ''But it doesn't look as if it's worked this year. It's earlier but not early enough.''
Though Ohio and Texas have been considered last stands for Democratic candidate Gary Hart, some Ohioans, such as Oberlin College freshman Patrick Corrigan, consider the race basically over. ''I really don't see all that much in anyone,'' the 18-year-old said Friday. But he added that he would vote for either Hart, Walter F. Mondale, or Jesse Jackson in November against President Reagan, whose Central America policies Mr. Corrigan dislikes.
The flagging interest has angered Ohio Senate president Harry J. Meshel, who pushed through last year's date change.
After February's New Hampshire primary, Senator Meshel demanded that Ohio's 1988 presidential primary be the nation's first, two weeks before any other. ''We have a state (New Hampshire) with an election that brings to the polls fewer people than a state Senate election in Ohio,'' Meshel said. ''This is not a put-down (of New Hampshire), but Democrats there haven't had anything but grocery stores for 40 years.''
In contrast, he argues, Ohio offers the small towns and farms of Sherwood Anderson's novels, the sprawling industrial cities that enriched Rockefellers and Firestones, and the test markets in Akron and Columbus where businesses sample their new products.
''If you wanted to send a foreigner to a single state that had within it most of the varying ways of life in America - a state that in its recent history had enjoyed some of the nation's greatest successes and faced some of its most difficult problems - you could not do better than to recommend Ohio,'' notes Michael Barone and Grant Ujifusa in ''The Almanac on American Politics 1984.''
Meshel, Brown, and several of the state's leading newspapers back the concept of a regional, Great Lakes-area primary that would offer a cross section of urban and rural, prosperous and poor, and liberal and conservative voters.
Gov. Richard F. Celeste and most state officials support front-runner Mondale. Hart, whose support has come in other states from upwardly mobile, well-educated voters, faces an uphill struggle in Ohio, which ranks 40th in the percentage of college graduates among its residents.
Jackson has limited his campaigning to the medium and larger cities, primarily the Cleveland-Akron area in the northeastern part of the state.
In the primary, voters will choose a candidate, but their vote goes toward a delegate in each congressional district. Hart and Mondale have delegates in each of the state's 21 districts, and Jackson in 19. Democratic candidate Lyndon H. LaRouche has delegates in 5.
George McGovern and Alan Cranston also have several delegates who, if elected , would be uncommitted.
President Reagan is running unopposed on the Republican side.