CLA is marketed as a fat burning product, and so it would not cause direct muscle loss or atrophy. Having reassured you on this note, I also would discourage you from taking CLA for other reasons. The main thing that supplements do is they take away the emphasis on exercise and diet, and this means that often the weight that can be lost is rapidly regained, because it is not lost by lifestyle changes. In the case of CLA, there is some evidence, but not a whole lot, that it actually works to start with. A very comprehensive study done a few years ago showed that the only effect was about a 1% reduction in body fat achieved in women only, and only when the starting body fat was high anyway. Therefore, the benefits seem to be pretty limited to begin with. All things considered, exercise and diet are definitely the way to go.

Good luck