I actually do know someone who lost twins because of amnio.  For some reason her sac was punctured and she just lost fluid for the rest of the pregnancy and the babies died within an hour of birth.  It’s a really horrible story but I just felt like I should answer your question.

On a much brighter note, I had amnio with my first child and CVS with my second, and had no complications (the CVS hurt a bit but the amnio didn’t even hurt).  I also know that complications are extremely rare.