Ideally, the officer who is first to respond to a crime scene should take complete control of the scene. By doing so, that officer will ensure that the evidence at the scene of the crime will not be destroyed or tampered with by anyone, whether purposely or accidentally.
When an officer arrives first at a crime scene, they are generally responsible for securing it. Of course, this may not be initially possible. The officer may need to help a victim. He or she may need to apprehend a suspect. These things will take priority over securing a crime scene and may even cause unavoidable damage to the evidence.
Once it becomes possible, the first officer on the scene needs to secure the scene. This often involves putting up barriers of some sort (police tape) to keep people out of the scene. The officer should prevent any non-essential personnel from entering the scene. They should also identify possible witnesses and ensure that the witnesses do not leave the scene before they can be questioned. In these ways, the first officer on the scene can (as much as possible) ensure security of the scene. This is their role with respect to security of the crime scene.