The latest poll shows Ohio Governor Ted Strickland is keeping a small lead over his Republican challenger John Kasich, 43% to 38%.
The poll released Tuesday by Quinnipiac University shows little change from its surveys taken in March and April.
The poll also finds that just over half of Ohio's voters give Strickland failing grades on his handling of the economy and the state's budget.
About half the voters also say they don't know enough about Kasich to offer an opinion.
The survey has a margin of error of plus or minus 3 percentage points.
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