The shots were reported somewhere outside the immediate area of the Cranbury Elementary School in Norwalk around 11:25 a.m., but a police investigation could not confirm that any shots were fired.
The entire upstate New York town of Bovina was placed on lockdown Sunday while police were engaged in a standoff with an armed man.
The school system in Newtown, Conn., was briefly placed on lockdown Monday, after someone made a threatening phone call to a school near the site of the Sandy Hook Elementary School massacre.
Counselors will be available at two schools in Newark a day after a student was gunned down and a school was put under lockdown.
The federal courthouse in Brooklyn was locked down Tuesday afternoon, after suspicious white powder was discovered.
Newsday reported that the suspect, who was caught in the Bronx, was wanted in connection with a shooting in November of 2011.
The principal of P.S. 4 called for the lockdown as a precaution after police said one child was overheard telling another that he brought a gun to school.
The lockdown was imposed Monday morning after a man called the Warren County communications center around 9:45 a.m. and claimed he was armed with an assault rifle and was in the woods behind Hackettstown High School.
Though the school decided not to close Friday, Smithtown West administrators assured both students and parents that they took the matter very seriously.