In research literature, colorblindness and handedness appear to be correlated through male-ness.
Genetic causes of colorblindness are on the X chromosome, which explains why males are much more likely to suffer from colorblindness than females, as high as 16x more likely for red-green colorblindness.
Handedness is a complex polygenic trait governed by dozens of genes. A recent paper, Brandler et al., PLOS Genetics 2013, studying handedness implicated genes in chromosome 10.
However, males appear to be 25% more likely to be left-handed than females.
I wasn't able to find any studies directly addressing whether or not handedness is correlated with colorblindness, but it appears that if the only thing you tell me is that you are left-handed, then I can guess that you are more likely to be male than female, which means you are more likely to be colorblind than a person picked at random. So yes, a correlation appears to exist through maleness.
However, it's possible that being left-handed is conditionally independent of being colorblind given that you are male. In which case, for males, there may not be a correlation between left-handedness and colorblindness - there haven't been any studies addressing this question that I have seen.
To put this another way: if you tell me that you're male and left-handed, then insufficient scientific studies exist for me to guess whether or not you're more likely to be colorblind or not.