A closure with a self-resealing elastomeric septum has a shutter slidable between a closed position over the septum and an open position for exposing the septum. The shutter is spring biased towards the closed position, and may be pushed and held away from the closed position with the tip of an oral syringe to gain access for penetration of the elastomeric septum. The closure may have an upper portion mounted to a lower portion fastened for closing a container. A conduit extends through the upper and lower portions to the interior of the container. A break-away connection is adapted to preferentially break or separate when a sufficient bending or twisting force is applied to the upper portion relative to the lower portion. The conduit may be normally closed by a self-resealing elastomeric septum provided in the lower portion and a slidable shutter may be provided on the upper portion.