Former Vice President Joe Biden Joe BidenOmar fires back at Trump over rally remarks: 'This is my country' Trump mocks Biden appearance, mask use ahead of first debate Trump attacks Omar for criticizing US: 'How did you do where you came from?' MORE and President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE are running neck and neck in Ohio, according to a new poll of the state released on Monday by Baldwin Wallace University.

The poll shows Biden with roughly 45 percent support in the Buckeye State, while Trump trails with just about 44 percent. That’s well within the survey’s 3.7 percentage-point margin of error, suggesting that the race in Ohio remains a dead heat.

Ohio is one of the most sought-after swing states in presidential elections. The state has voted for the eventual winner in every presidential race in recent history. Former President Obama won the state twice, in 2008 and 2012, before Trump flipped it for Republicans in 2016.

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Some strategists and operatives on both sides of the aisle, however, believe Ohio has developed more of a Republican bent in recent years. Not only did Trump win the state four years ago, but Democrats lost a key opportunity to flip control of the governor’s mansion in 2018, when Republican Mike DeWine beat out Democrat Richard Cordray Richard Adams CordrayConsumer bureau revokes payday lending restrictions Supreme Court ruling could unleash new legal challenges to consumer bureau Supreme Court rules consumer bureau director can be fired at will MORE to succeed former Gov. John Kasich (R).

Still, the new Baldwin Wallace poll suggests that Ohio is still in play for Biden.

Forty-nine percent of respondents in the poll said they approve of the job Trump is doing in office, while just as many said they disapprove.

Trump remains far less popular with Ohio voters than DeWine, who has taken on new national prominence amid the coronavirus pandemic. Eighty-five percent of respondents said they approve of DeWine’s handling of his job, while only about 11 percent said they disapprove.

Among self-identified Democrats and Democratic-leaning voters in the state, Sen. Elizabeth Warren Elizabeth WarrenHarris joins women's voter mobilization event also featuring Pelosi, Gloria Steinem, Jane Fonda Judd Gregg: The Kamala threat — the Californiaization of America GOP set to release controversial Biden report MORE (D-Mass.) is the most popular choice to serve as Biden’s eventual running mate in the November election. Forty-seven percent said they would like to see Warren as Biden’s vice presidential pick, according to the survey.

Sen. Kamala Harris Kamala HarrisButtigieg stands in as Pence for Harris's debate practice First presidential debate to cover coronavirus, Supreme Court Harris joins women's voter mobilization event also featuring Pelosi, Gloria Steinem, Jane Fonda MORE (D-Calif.) was the next most popular choice for the running mate role with 41 percent of those respondents supporting her.

The Baldwin Wallace University poll surveyed 797 self-identified registered voters in Ohio online from April 20-25. It has a margin of error of 3.7 percentage points.