Newtown police say the threat was made around 9 a.m., prompting an evacuation.
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Lt. Aaron Bahamonde said there was a heightened level of anxiety in town on the anniversary, and the school superintendent decided to cancel remaining classes.
It's unclear whether the threat was related to the bomb threats made nationwide Thursday.
The school where the shooting happened on December 14, 2012, was knocked down, and a new building was constructed at the same site.
Remembering the victims of the Sandy Hook school shooting:
Moments of silence were observed in Newtown and other places Friday morning in memory of the victims, and bells at a local church were rung at 9:30 a.m.
All town offices in Newtown were closed from 9:30 a.m. to 9:45 a.m. Friday for a moment of silence and period of reflection.
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Gov. Dannel P. Malloy has ordered all state and U.S. flags to remain at half-staff in remembrance of the victims. The flags have been lowered in honor of the late President George H.W. Bush.
An interfaith memorial service is scheduled for 7 p.m. at Congregation Adath Israel of Newtown.
(The Associated Press contributed to this report)