Tea tree oil should be used in a diluted form. It's reported in the literature that a 10% solution is safe, and effective in chronic dermatitis and pruritus skin conditions in dogs (i.e. 70% success rate). It's also useful in alopecia (hair loss).

I used tea tree oil on my previous dog (1/2 Lab, 1/2 Golden) by applying a thin film on top of some antibiotic salve to deter licking of the salve. She gave it a short lick, and then gave me a dirty look. I have no idea what that thin film represented per what she ingested. As with all substances, the individual will have a different tolerance level to it. Some dogs are extremely sensitive to it, while others are not.

Also note the turpenes in tea tree oil can be absorbed through the skin. The dog does not have to lick or ingest it for the turpenes to get absorbed systemically. Tea tree oil especially in undiluted form can cause a burning sensation on open wounds. I wouldn't want to apply it even diluted to an open wound.