Hair dye contains chemicals that can be absorbed by the skin, so you should be careful when coloring your hair.

The American Cancer Society advises:

• Follow packaging instructions, especially portions containing warnings and precautions.
• Before dyeing hair, do a patch test to check for a skin reaction. Do this even if you have used the same dye before.
• Wear gloves when applying dye.
• Never mix different dyes.
• Leave the dye on only for the recommended amount of time. Rinse thoroughly.
• Never dye eyebrows or eyelashes.

Source: HealthDay