Two people were arrested outside a Bayport school at around the same time classes were letting out Wednesday, according to police.
The pair was trespassing on school grounds at Sylvan Avenue Elementary School, police say.
One was in possession of a hypodermic needle, according to authorities.
Parents are calling for video cameras, locks on gates and additional security guards.
The school currently has one guard on duty, according to parents.
Jennifer McCormick says she and many other parents have been asking the district to increase security since the Sandy Hook Elementary School massacre in Connecticut three years ago.
Photos taken by parents a day after the arrests appear to show that doors and gates were unlocked or propped open around school grounds.