Hillary Clinton led Donald Trump by 1 percentage point, 46-45, in a two-way race for North Carolina, according to a new Bloomberg Politics poll.

Clinton also bested Trump by 1 percentage point, 44-43, when third party candidates were included in the survey.

"It's hard to imagine a battleground state where things could be much closer, both in the overall horse-race number and in the underlying party ideology of the voters," said pollster J. Ann Selzer, who directed the survey, to Bloomberg. "This is the kind of situation where third-party candidates could tip the balance."

Trump is leading the battle for independent voters, indicating North Carolina may be decided about who can turn out their base in greater numbers. Trump has a 26-percentage-point advantage on Clinton among independents, a 51-point lead among whites without college degrees and a 24-point edge with evangelical Christians. Clinton has a 67-point advantage on Trump among non-whites, a 37-point lead among voters under age 35, and a 17-point edge with women.

Selzer and Co. conducted the survey for Bloomberg Politics from Sept. 29-Oct. 2, after the first presidential debate. The poll surveyed 805 likely voters and had a 3.5-percentage-point margin of error.