I made a model but when rigged it doesn't move correctly So I made a model with a mirror modifier but realized that when I rigged it the arms would move in sync. So I remove the mirror modifier and copied the left side of the model to make the right side. but when I rigged it and started to move the bone that moves the neck and head the neck and head start to split in half. (Graphic I know, but I also made sure that both sides of the mesh where connected using Ctrl+J) 

How to i make the rig move both left and right sides of the head and neck.

Here is a video of whats happening. https://youtu.be/R6cnYOal2Kw 

The video is a little outdated so some of the problems where fixed like the T-Pose. But other than that I am new to blender and barely know what i am doing.
Ctrl J has the only effect to put all vertices (from two different "container"-objects) into one "container-object" only, but both half of the mesh will have thier own central line vertices. You can merge them selecting all vertices and using the "remove doubles" option.