I do not know your study, or your sample size, or the nature of your measures, or the statistical analyses you intend to perform. So there is not much for me to comment on. But generally speaking, "dependent" variables do not need to be normally distributed, and I cannot remember any instance where it was required that "independent" variables should be normally distributed.
Since Karabiner hasn't explicitly said it - if you're doing regression we don't require any of the input data to be normally distributed. It is the error term which we put the normal distribution assumption on. So if you want to test for normality then it makes the most sense to test the residuals from the model.