I live in MO and did STD for my BA last year. Never told them exactly what I was having done, I just said I was having surgery. The nurse said she needed a note from the Dr. stating I would be under his care from <date> to <date>. FMLA would be similar, where the Dr. would fill out a form that HR sends you (again, because you are having surgery and need to recuperate) stating how long you need to be off. Unfortunately you will need notes from the Dr. to get this done. Some are slow filling the paperwork out, and some charge for each one (my oncologist charges $25 for FMLA paperwork, i. e.).
I talked with HR for my GCS this summer and am taking vacation for the time I am under Brassard's care, then having my Primary doc (she is so cool!!) write a note that I will be under her care for the following month. So, that way I avoided having to ask Dr. Brassard for a Dr.s note for STD while in Montreal.
The bottom line is that you do not have to tell them exactly what you are having done, only that you will be recovering from a procedure and let the Dr.s note speak to the necessity of it. At least that is how my company handles it, and what I believe HIPAA dictates. They even told me that I do not have to tell my boss that I will be out on STD, HR will notify her of my absence (of course, I am up front with my boss and she is supportive, so I don't play that game with her, but I could.

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Hope that helps a bit!