How do I lock a certain Axis on a drag object script?

Currently I can drag my object which uses a CharacterController (Don't want to use Rigid body) and I can drag it around my scene. How would I make it the object movement be locked only for a certain Axis, for example: on Axis Z?

The drag object movement script I'm using is:

 var speed: float = 10;  // speed 
 private var dragObj: Transform = null;
 private var hit: RaycastHit;
 private var length: float;
 private var character: CharacterController;
 
 function Update(){
 
     if (Input.GetMouseButton(0)){  // if left mouse button pressed...
         // cast a ray from the mouse pointer
         var ray = Camera.main.ScreenPointToRay(Input.mousePosition);
         if (!dragObj ){  // if nothing picked yet...
             // and the ray hit some character...
             if (Physics.Raycast(ray, hit)){
                 character = hit.transform.GetComponent(CharacterController);
                 if (character){
                     dragObj = hit.transform;  // save picked object's transform
                     length = hit.distance;  // get "distance from the mouse pointer"
                 }
             }
         } 
         else {  // if some object was picked...
             // calc mouse pointer displacement
             var mov = ray.GetPoint(length) - dragObj.position; 
             // set object velocity
             character.Move(mov * speed * Time.deltaTime);
         }    
     }
     else {  // no mouse button pressed
         dragObj = null;  // dragObj free to drag another object
     }
 }