CTS is a repetitive stress injury. That means there has to be some injury to cause it. Genes, while they may cause some other nasty medical problems, do not cause repetitive stress. They can, however, make it more likely that you will develop CTS.
CTS is the aggravation of tendons passing through the Carpal Tunnel. So basically, if you are genetically disposed to have a small Carpal Tunnel you stand a much greater risk of developing Carpal Tunnel Risk. It may be to the point that even basic wrist movements cause repetitive stress, but it is still your actions and not the genes that cause the injury.

