using UnityEngine;
using System.Collections;

public class PlayerManager : MonoBehaviour   
{

                   
   private ObjectManager ojm;

   public int playerDamge = 10;

   void Start ()   
   {
     
   }

   void Update ()   
   {
    if(Input.GetMouseButtonDown(0))
    {
     RaycastHit hit;
     Ray ray = Camera.main.ScreenPointToRay(new Vector3(Screen.width/2,Screen.height/2,0));
     bool isHit = Physics.Raycast(ray, out hit, 1000);
     if(isHit == true)
     {
      Debug.Log(hit.transform.tag);
     }

     if(hit.transform.tag == "Objectgame")
     {
                     //Отнимаю здоровье у объекта
      ojm.Health -= playerDamge;
                     //Здесь выдает ошибку.
     }
    }
     
   }
}

using UnityEngine;
using System.Collections;

public class ObjectManager : MonoBehaviour {
     

   public int Health = 100;

   void Start ()   
   {
    Health = 100;
   }

   void Update ()   
   {
    if(Health < 0)
    {
     Destroy(gameObject);
    }
   }
}

ojm.Health -= playerDamge;
Вот здесь