In my 2004 330Ci ZHP with 88k miles:

I started to notice a hissing sound when my A/C was turned on, which was especially noticeable right when the car was turned off or when the A/C was switched on or off. A/C was still blowing cold. Adjusting the fan speed didn't affect the sound, and the sound would disappear when the A/C button wasn't activated.

The sound was similar to the high pitched sound of a CD drive. I took this into my local shop, and had them run an A/C diagnostic. They recharged the A/C (with dye) and noticed that it was little low. The diagnostic and re-charge cost around $200, though this includes the next appointment should there be an issue.

Low and behold, it turns out that this recharge solved the problem (for now). I will keep an ear out for the return of this sound, and if so, we now have dye in there to see where the leak in the A/C system is. Really hoping it isn't the evaporator and that it was as simple as a low charge.