There is a possibility, but not if you go about it correctly. All hair dye packaging recommends carrying out a skin patch test before using a colorant. Apply the color to an area the size of a quarter, behind an ear or inner elbow. If, after 24 hours, there is no irritation, discomfort or redness, it is safe to color without risk of a rash or reaction. When you read about people suffering severe allergic reactions, it is most likely that the patch-test warnings have been ignored in these cases.