Tea Tree Essential Oil is toxic to dogs but only in it's undiluted form.
You can safely apply Tea Tree Oil to your dogs fur or skin if you dilute it first with some water to bring the toxicity of the Tea Tree Oil down first.
I've used diluted Tea Tree Oil on my dogs fur and skin to help kill fleas and ear mites after I've diluted the Te Tree Essential Oil.
If you put the Tea Tree Oil on your dog without diluting it first then it can get into the dogs skin and bloodstream and poison the dog but when it's been diluted it won't harm the dog.