I've heard that there is a correlation with being left-handed and left-eyed and vice versa. Pick up a camera or a piece of paper with a hole in it and bring it quickly to your face. Which eye is used? Does this correlate with your strong hand? Sometimes, when one is right-eyed and left-handed or vice-versa, this is called "cross dominance".
Some psychologists say that this will create problems in behavior.
Don't know if that is true. Ambidextrous people seem to fare all right.