It seems obvious that a cat scratch could transmit germs to your pup, and that those germs could in turn cause a rash. However, the scientific research and evidence in this area is sparse. It's hypothetically possible that your kitty's claws are what's ailing your pooch, but there's only conclusive proof of a very few ways this is possible.
Cats and dogs can't transmit most pathogens to each other because they're different species. This is true of most infectious diseases -- such as distemper, parvovirus, feline leukemia and the other biggies your pets are vaccinated against -- but it's not so simple when it comes to normal skin or surface fauna. Skin or surface fauna are the bacteria and fungi normally present on your pet's pelt. They don't cause any problems for a healthy pet, but when they're introduced into broken skin, such as by Miss Kitty's claws, they may indeed cause an infection or inflammation, including a rash. Your cat also collects all kinds of bacteria under her nails from digging in cat litter or soil and can transmit these to her hapless victims. Any uncleaned wound can become infected by these opportunistic bacteria and fungi.
Cat Scratch Fever?
Despite what you may have been led to believe, there's nothing sexy about cat scratch fever. It begins with painful swelling in the scratch and an itchy, painful rash, and can progress to lymph node swelling, fever and systemic infection. This condition is caused by Bartonella henselae bacteria in cats and it's transmissible to humans. There's a very rare strain that's been passed from dogs to humans, and it's also possible for dogs to catch the feline strain from cats. Confirmed cases of cat-to-dog transmission are few, but this may have more to do with how few people are looking than with the actual numbers of cases.
Allergic to Cats?
Is it possible your puppy's rash is caused by an allergy to your cat? Again, it's hypothetically possible, but almost no research has been done in this area. Most cat allergies are allergies to kitty saliva, which is present on your cat's paws and claws. A cat scratch is an excellent way to deliver this allergen to your pup's sensitive skin. If you know your dog's skin reactions occur each and every time he winds up on the wrong side of Fluffy's claws, talk to your veterinarian. She can help you determine whether your dog is allergic and advise possible treatments.
Assessing the Damage
There are a very few rashes that can pass from your cat to your dog without claws involved. These are tick-borne illnesses, including Lyme disease -- caused when an infected parasite drops off one pet and attacks another -- and they require immediate veterinary attention. A veterinary consultation is a good idea any time your dog is suffering from rashes and inflammation, regardless of the ultimate cause. If it turns out your cat's claws are the source, some form of intervention -- including behavior modification -- is in order.