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.
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.