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On most cars you would add fluid through the dipstick, but as the C6 has the tranny in the rear I guess there is no dipstick. My guess would be there is a fill hole on the side of the trans case, but better wait for someone to confirm what side it is on or even to post a pic.
There is a special procedure for checking and changing
the transmission fluid. Because this procedure is
difficult, you should have this done at the dealership
service department. Contact your dealer for additional
information or the procedure can be found in the service
manual. To purchase a service manual, see Service
Publications Ordering Information on page 7-14.
If it's like the C5, your trans must be at normal temp (86'F-122'F or something close to that) and the engine RUNNING. As mentioned above, remove the top plug when trans fluid at proper temp and engine idling. If fluid dribbles out, let it go- you were slightly overfilled. If no dribble, add fluid until full. Do NOT shut the engine off until the plug is back in place; otherwise you'll get a quart or two of hot fluid puking out the hole.
Thanks for the info. There is only one plug that I can find. It's a large plug OFF the bottom, Midway up. I do not have manual thats why this forum is great. It seems like a lot of pepole would change the oil every 10,000 mi or so, running the kind of power I see them making. Thanks to all.
This forum is a great place for info, but trusting your transmission to the word of others without confirming it in your own service manual might not be the most prudent course of action.
Get a set of manuals if you're going to be doing work on your own car. They actually make for some very interesting reading.