According to thecityofraleigh.gov, dogs and cats are not allowed within the city limits without a leash. If domesticated animals are not walked on a leash, they must be confined to their owner's. This includes parks as well. Dogs are not allowed off the leash in Raleigh parks, and they are not allowed on play grounds. Allowing pets to run freely within the city limits of Raleigh could result in a misdemeanor.