I'm having a problem with static, but seems like my cdp doesn't mind (so far). I have a wool rug and build up charge like crazy-sometimes I see the spark fly 1/4 inch.
I have tried to remember to ground myself... in fact, I ran a ground wire to touch before I touch my cdp, but don't remember to do it.
I guess it depends on the player (the chassis of my player is very heavy... lots of metal to keep ambient charges away from delicate circuitry).
good luck,