Don't delay a formal announcement
The news that a fatality has occurred should come from the company as soon as you know someone has lost their life. The only detail you need to release at this moment is the fact that an employee (or a contractor) has died. This is not the time to release names, details of the accident or any other specific information that can come later.
You need to make this acknowledgement because it changes the nature of the story. For example, if you have a large plant that has an explosion, it will make news. Explosions are newsworthy as reporters love fire. But an explosion that kills someone is a completely different story with a vastly different impact on people. Given that all journalism is about how events impact people, you can see how a fatality changes the story.
Don't ignore the obvious
Is a medical examiner's or coroner's vehicle at your facility? If so, the media doesn't need to have you tell them someone's dead. Those trucks don't just drive around hoping to come across a corpse. If the coroner is there, someone's dead. Not confirming the obvious makes you look incompetent.
One more thing that's important for communicators to keep in mind when a tragedy strikes. In a lot of cases, the leadership of the facility has a personal relationship with the deceased. They're friends, they may play on the softball team together. Maybe they went to school together. If that's the case, then your leadership may be in shock and unable to rationally or quickly make the right call. Talk through this with your management ahead of time. Have clear protocols. Understand that people will be hurting. Get as much room to do what you need to do independent of approvals and stick to your plan.
The goal of this post isn't to rush you into communicating. It's to prevent you or someone on your team from making an awful day worse.