Naugatuck police said they are investigating social media posts by "clowns" that mentioned the town's school district.
As a precautionary measure, Naugatuck schools will have added security and police presence on Tuesday.
Police said they do not believe the threats are credible, however, they are still investigating.
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Earlier, New Haven schools said it was prohibiting clown costumes during the Halloween season following a number of clown-related Instagram posts.
The Naugatuck PD is asking anyone that might have information regarding these posts to contact the Naugatuck Police Department at 203-729-5221 or the NPD Confidential Tip Line at 203-720-1010.