Update, 3:25 p.m.
Chappaqua schools Superintendent Lyn McKay also noted the stepped up police patrols, including for the district's schools. In addition, more school staff were stationed near building entrances.
"First of all, we are saddened and horrified by this event," McKay said.
New Castle Police are stepping up security , Lt. Daniel Cannon confirmed.
Police have been in touch with the Chappaqua Central School District about the matter, Cannon said, and explained that they are working very closely.
Cannon said that police and the district are "taking all appropriate steps," to assure safety at the schools.
While Cannon did not want to get into specifics, he did say that measures include more police patrols and providing more police resources to the school district.
Cannon does not feel there is any imminent threat locally, saying there is "no reason" to believe the Newtown shooting is related in any way to New Castle.
Chappaqua schools Superintendent Lyn McKay could not be reached for commment as of initial publication time.
Next door, Mount Kisco police report that no order has been given to provide extra security for the Bedford Central School District.