Nosebleeds do not occur spontaneously in cats. However, the nasal cavity is extremely sensitive and bleeds easily when traumatized. Most nosebleeds are associated with a blow to the face that damages the nose. Others are due to an erosion of the nasal membrane caused by a foreign body, infection, tumor, or parasite. Rarely, a nosebleed may be a manifestation of a generalized clotting disorder such as that produced by a low platelet count, liver disease, or exposure to rodenticide anticoagulants.
When a cat’s nose bleeds as a result of trauma, a midline fracture to the roof of the mouth may also have been incurred. Suspect this if the cat exhibits open-mouth breathing. This fracture can cause misalignment of the teeth, in which case the alignment must be adjusted and the teeth wired together to stabilize the upper jaw until it is healed. Any cat who has a nosebleed after trauma to the nose should be seen by a veterinarian.
Toxoplasmosis is a disease caused by the parasite Toxoplasma gondii, which can be found in garden soil and raw meat. Cats can get toxoplasma infection by killing and eating infected prey. The disease can also be passed on from cats to humans.
Treatment: Nosebleeds may be accompanied by sneezing spasms that aggravate the bleeding. Keep the cat quiet and confined. Apply ice cubes or cold packs to the bridge of the nose to reduce blood flow and aid clotting. Slight bleeding usually subsides quickly, especially if the cat is kept quiet. Persistent bleeding is a cause for concern. Call your veterinarian.
WebMD Veterinary Reference from "Cat Owner's Home Veterinary Handbook"