Yes all dogs mush be leashed any loose dog will be fined. There is also a pooper scooper law stating that you must pick up after your dog when you are walking it on a public way or any other area that is not your property. Be a good neighbor do not allow your dogs to use other peoples lawns for a bathroom.
There are no dogs allowed on school ball fields or the playgrounds. This is also a fineable offense. When entertaining the thought of allowing your dog to run and play in these area's, Think of the children who are using these places for ball games and other school related things. They don’t want to clean dog poop off their clothes or shoes that is why this law was put into effect.
There are no laws pertaining to cats, except that they must be vaccinated for rabies. Cats are free roaming animals.