Tea tree oil is not just toxic to cats:
http://www.petpoisonhelpline.com/poison/tea-tree-oil/
Tea Tree Oil
Poisonous to: Cats, Dogs
Level of toxicity: Generally moderate to severe, life-threatening
http://www.aspca.org/Pet-care/ask-the-expert/ask-the-expert-poison-control/tea-tree-oil.aspx
Tea tree, or Melaleuca alternifolia oil, does have toxic potential, depending on the circumstances of exposure.
http://www.wisegeek.com/what-are-the-dangers-of-tea-tree-oil-for-dogs.htm#
According to some veterinarians and animal experts, tea tree oil may be toxic for dogs when its ingested or absorbed through the skin. It is also suspected that using tea tree oil for dogs may also cause liver damage. Accidental ingestion of tea tree oil may cause gastrointestinal symptoms in dogs as well. Additionally, there have been reports of dogs suffering from neurological damage from the use of this oil.
This place prescribes it, but says not to apply where animal can lick/ingest. You find that part on your basenji, let me know since if they can get their paws to it, they can still rub and lick it off:
http://www.vcahospitals.com/main/pet-health-information/article/animal-health/tea-tree-oil/578
Like other essential oils, tea tree oil can be toxic if ingested. Since the maximum safe dosage has not been determined, most doctors recommend using it topically, and then only in dilute form. Tea tree oil is so potent in its antimicrobial effects that even a 1:250 dilution appears to be effective and yet quite safe for use as an ear wash. Tea tree concentrations in anti-fungal shampoos for dogs and cats are often even lower. Never apply tea tree oil directly to the skin without diluting it. NEVER APPLY IT to areas that the animal can lick. Safety in young children, pregnant or nursing women, or those with severe liver or kidney disease has not been established. Use with caution in similar situations in pets.
http://www.beaverlakeah.com/site/view/63679_TeaTreeOil.pml
According to National Animal Poison Control Center, the use of tea tree oil in dogs has been associated with hypothermia, muscle weakness, ataxia, tremors, altered behavior, paralysis. Cats are also sensitive to the tea tree oil compounds. A case report has been published in which three cats had clinical signs and one cat died after being treated with the oil.