Nope. I signed nothing. I'm very familiar with what is in my personnel file as I worked in a position where I had access to my file and could and did look at it at will.Why not ask the school district? I believe they were supposed to offer you the choice and document your answer. You may have caught them having slipped up and you may have some recourse. Or, they may pull your file and show you where you signed a slip saying you chose to opt out and you've forgotten (as I most likely would have ).
You won't know unless you ask.
New employees does sign that medicare form.
To make sure, I am going to ask a friend to access my records to make sure I did not overlook it. I am going to ask her to look at my friend's also and go from there.