Very much so.
Permanent black hair dye is linked to causing leukemia and lymphomas.
Chemicals can enter the body through the skin.
Google: Teen 'feared she would die' after reaction to hair dye
The allergic reaction was caused by a well-known brand of semi-permanent hair dye Chloe used to turn her hair black for a Hallowe’en party. . . . . called for beauty bosses to ban hair dye chemical PPD (para-phenylenediamine) from the shelves. 11-04-11
The chemical is not new and is present in a number of brands of dark hair colours, acting to help adhere the dye to the hair so that it doesn't wash out. It’s made from coal tar and is used in both permanent and semi-permanent hair colours. It’s well-known to be a cause of serious allergic reactions -- including something called contact dermatitis which can lead to rashes, blisters, and open sores.
PPD is sometimes added to black henna tattoos and that using them is not safe. Allergic reactions usually begin within two to 10 days following application. One bad reaction can lead to sensitivities to other products such as hair dye, sunblock and some types of clothing dyes. Oftentimes, it's using the product a second or third time.
Google: A 38-year old mother left in a coma after using hair dye. 11-22-11. SHE DYED HER HAIR MANY TIMES BEFORE, USING THE SAME BRAND.
Playing with chemicals is not like playing with clothes, or doing a manicure, there are penalties for playing chemicals in the lab. Even hair color experts at the salon are not rocket scientists, they do a bang up dye jobs to their clients or their own hair.
Example: "My hair is right about armpit length as it is, but I've severely damaged it by bleaching it all at once. As a student of cosmetology myself, I would have to say that it was probably one of the worst mistakes I could have ever made."
Another example: ok i did my hair yesterday i DIDN'T bleach it ,but im not sure what its called but she took the color out of my hair and then dies it a blond color and my head was on fire it killed me so after that i hated my hair color so i colored it my self a darker color, it looked so ugly and it burned me again it rully hrt so after i washed it my mom checked it for me and found small spots of blood all over my top scalp like over 20 of em now im scared and don't know why its there is it from the color am i sick and something is wrong ??
Google FDA.gov & search for Hair Dye & Relaxers.
Google: Hair Dye FAQ's Are Hair Dyes Safe?