wesleysgirl

It could be soy sauce mixed with ponzu, a Japanese citrus. Kikkoman Ponzu is a commercial form of it mixed with soy sauce.

http://en.wikipedia.org/wiki/Ponzu

But the sauce that typically comes with dumplings in a Chinese restaurant is probably mixed in house: soy sauce, watered down a bit, plus some rice vinegar and Chinese hot chili oil, and probably some grated fresh ginger if you can taste ginger.
http://chinesefood.about.com/od/saucesdipping/r/dumplingsauce.htm

Also see:
http://en.wikipedia.org/wiki/Jiaozi