Mr. Paleologos noted that there is a sharp contrast between how the candidates perform in urban centers such as Cleveland, which favors Mrs. Clinton, and the outer counties that lean toward Mr. Trump. Although the addition of Gov. Mike Pence as Mr. Trump’s running mate has not had an immediate impact, Mr. Paleologos suggests that it could help him in areas that border Mr. Pence’s home state of Indiana.

Terrorism and the economy, which are seen as strong areas for Mr. Trump, remain the most important issues to voters in Ohio. Mr. Trump’s proposal for a temporary ban on Muslim migration has not turned off voters, as 48 percent support the idea and 45 percent oppose it.

Third-party candidates could end up being the deciding factor in the race in Ohio, as the 5 percent of the vote that Mr. Johnson is getting is siphoning more support away from Mr. Trump than it is from Mrs. Clinton.

The poll had a margin of error of plus or minus four percentage points.