Copied from the CDC website (Centers for Disease Control and Prevention)

What happens if a neighborhood dog or cat bites me?

You should seek medical evaluation for any animal bite. However, rabies is uncommon in dogs, cats, and ferrets in the United States. Very few bites by these animals carry a risk of rabies. If the cat (or dog or ferret) appeared healthy at the time you were bitten, it can be confined by its owner for 10 days and observed. No anti-rabies prophylaxis is needed. No person in the United States has ever contracted rabies from a dog, cat or ferret held in quarantine for 10 days.

If a dog, cat, or ferret appeared ill at the time it bit you or becomes ill during the 10 day quarantine, it should be evaluated by a veterinarian for signs of rabies and you should seek medical advice about the need for anti-rabies prophylaxis.

The quarantine period is a precaution against the remote possibility that an animal may appear healthy, but actually be sick with rabies. To understand this statement, you have to understand a few things about the pathogenesis of rabies (the way the rabies virus affects the animal it infects). From numerous studies conducted on rabid dogs, cats, and ferrets, we know that rabies virus inoculated into a muscle travels from the site of the inoculation to the brain by moving within nerves. The animal does not appear ill during this time, which is called the incubation period and which may last for weeks to months. A bite by the animal during the incubation period does not carry a risk of rabies because the virus is not in saliva. Only late in the disease, after the virus has reached the brain and multiplied there to cause an encephalitis (or inflammation of the brain), does the virus move from the brain to the salivary glands and saliva. Also at this time, after the virus has multiplied in the brain, almost all animals begin to show the first signs of rabies. Most of these signs are obvious to even an untrained observer, but within a short period of time, usually within 3 to 5 days, the virus has caused enough damage to the brain that the animal begins to show unmistakable signs of rabies. As an added precaution, the quarantine period is lengthened to 10 days.