Sorry, I'm not there yet. But I'm going to approach my employer first to give me a copy of every communication with DOH because I might need them later. I'm hoping that they'll give it to me.
I'm also going to get a copy of the form employer fills out. This should be available from DOH's web site and see if it says it should be confidential.
If employer is sincere, they should not have problem giving copy to you. If they don't I would be concerned and look for some place else after 3 years are up.
You can call DOH and the should be able to tell you if they got report or not. If DOH donot give you a copy, they can at least tell you if it was satisfactory. And you can tell them you need for as proof as employer would not sign for you. This would be the extreme case and I would wait until last report is filed.
I'll let you know what happens when I encounter this.