A poll released on Thursday shows that Montana Republican Senate candidate Tim Sheehy has overtaken Sen. Jon Tester in a race that could decide the balance of power in the U.S. Senate.

The poll from Emerson College and The Hill found that roughly 48% of Montana voters supported Mr. Sheehy, an aerospace millionaire handpicked by the GOP to topple Mr. Tester, compared to 46% who backed the three-term incumbent.

However, the results of the poll had a margin of error of plus or minus 3 percentage points, meaning that the candidates were virtually tied.

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About 5% of the polled voters were undecided in the battleground race, a 9 percentage-point drop from the previous survey conducted by Emerson College in April.

“The share of undecided voters has decreased from 14% to 5% as November draws closer, and Sheehy has benefited with a six-point increase in support, while Tester’s support has only increased by two points,” said Spencer Kimball, executive director of Emerson College polling.

The poll was conducted Aug. 5-6 and sampled responses from 1,000 Montana voters. About 43% of the surveyed voters were Republicans.

While Mr. Sheehy gained ground on Mr. Tester, former President Donald Trump’s grip on Montana slightly weakened in a matchup with Vice President Kamala Harris.

Mr. Trump’s lead in Montana dropped by 1 percentage point, to 55%, while Ms. Harris gained 5 points and jumped to 44% compared to when President Biden was at the top of the ticket.

The former president has dominated Montana in the past two elections, clinching the state in 2016 by 20 percentage points and by 16 points in 2020.

Mr. Trump, who endorsed Mr. Sheehy earlier this year, is slated to hold a rally Friday for the political newcomer in Bozeman, Montana.

The GOP hopes that Mr. Trump’s popularity in the state, coupled with an influx of new voters since Mr. Tester’s last reelection bid in 2018 that skew largely Republican, will propel Mr. Sheehy to victory in November.