Obama's advantage is within the CNN/ORD International poll margin of error.
The latest results, released Friday, show support for the candidates "essentially unchanged" since early October, said CNN Polling Director Keating Holland.
The gender gap between the men also remains the same. Obama is favored, 56 percent to 42 percent, among women, while men prefer Romney, 50 percent to 44 percent.
Among independent voters, Obama is preferred 49 percent to 44 percent.
Early voters gave Obama a 59-to-38 percent lead, while Romney led among those who said they will vote on Election Day, 51 percent to 44 percent. Four percent said they could change their minds.
The poll found Obama gaining among young, lower income and urban voters and losing support with older voters, suburbanites and higher-income voters.
The survey of 1,009 Ohio adults -- including 896 registered voters and 741 likely voters -- was conducted by telephone Tuesday through Thursday after Monday's presidential debate.
The margin of error is 3.5 percent.