An emailed threat said bombs had been planted in the homes of Springfield's mayor and other city officials, spokeswoman Karen Graves said on Friday.
A second email said bombs would be detonated at locations including Springfield City Hall, a high school, a middle school, two primary schools, a local office of the Ohio Bureau of Motor Vehicles and a licensing bureau.
The buildings were evacuated, and authorities with explosive-detection dogs swept and cleared them, officials said.
"We are committed to the safety and well-being of our community and take all threats to public safety with the utmost seriousness," Graves said.
"We are currently collaborating with the Dayton office of the Federal Bureau of Investigation to determine the origin of these email threats."
The Springfield City School District said in a statement on Friday that "all threats to the Springfield City School District are taken seriously and will be prosecuted at the highest levels. The district's messaging to families continues to be one of gratitude for their patience and understanding as our Wildcat Family navigates these events".
The threatening emails referenced an influx of thousands of Haitian immigrants into the predominantly white, blue-collar city of about 60,000, about 70km from the state capital of Columbus.
At Tuesday's presidential candidate debate with Vice President Kamala Harris, Trump repeated debunked claims about Haitian immigrants eating cats and dogs. Trump's comments echoed similar claims made by his campaign, including his running mate, Ohio Senator JD Vance, and other Republicans, including one that immigrants are eating fowl snatched from public parks.
In March, unsubstantiated rumours started circulating that three Haitian men were seen in a Springfield park grabbing a duck and a goose. In recent days, a sign was posted at the park saying "Please Do Not Eat The Ducks."
Workers on Friday removed the unauthorised sign, which looked professionally made, said Brad Boyer, deputy director of the National Trails Parks and Recreation District.
In an interview with NewsNation on Friday, Springfield Mayor Rob Rue said the claims are "just untrue," and cast the city in a negative light.
"Springfield is still beautiful and your pets are safe," he said.
"There's a lot of frenzy on the internet, but this is not what we're seeing. It's a bit frustrating."
Rue acknowledged the immigrant influx is straining police, hospitals and schools. He said the city asked for help several months ago.
"There is a culture clash, and we see it, and we know it," he said.
"And the federal leaders who had the national stage did not help us solve this problem."
