The (Cleveland) Plain Dealer and Ohio Newspaper Poll said both candidates had 49 percent of the vote in the state, which is considered a key swing state with enough electoral votes to be potentially decisive.
The same poll Sept. 23 had Obama with a 5-percentage point lead.
The Plain Dealer said Ohio has been awash in political advertising and campaign workers have been scouring the state to make sure every possible voters makes it to the polls on Election Day.
The small number of undecided voters so late in the game has made rallying likely supporters a major priority for both campaigns.
"Absent any more twists and turns, a remarkable presidential campaign may end with the campaign that executes the best ground game, narrowly delivering Ohio for the next president of the United States," said Eric Rademacher, co-director of the University of Cincinnati Institute for Policy Research.
The poll released Sunday was conducted by telephone Oct. 18-23 among 1,015 likely voters. The margin of error was pegged at 3.1 percentage points.
The Plain Dealer said some of the respondents were contacted before the Oct. 22 presidential debate but it did not appear reaction to the debate influenced the overall poll results.