When he and his wife tried to get the dog away from the cat, which was on a leash, they were both bitten, he said. The neighbor still has the pit bull.
Carson said the dogs, which destroyed the gate to the fence surrounding his property, still get into his yard.
Councilwoman Susan Saum-Wicklein said a child should be able to play in a fenced-in yard without fear of being bitten by a dog.
Saum-Wicklein was surprised to learn that there is no penalty in animal control regulations for a dog biting a child or damaging property.
"It is illegal to let your dog run loose," said Mike Heyser, city building inspector.
If a dog bites someone it becomes a health issue and the animal can be quarantined to check for rabies, said Marc David, a city code enforcement officer.
The Washington County Society for the Prevention of Cruelty to Animals is responsible for enforcing animal control regulations, city officials said.
Carson said the SPCA showed up two out of the seven times he called to complain about the dogs on his property.
Carson asked city officials to consider limiting how many dogs a city resident can keep.