I know of no California statewide law or regulation which limits the number of pit bulls a household can own or keep on their property. In this last sentence I refer to situations in which none of the dogs have been determined by the local animal control authority as being "potentially dangerous" or "vicious". Your county or city might have an animal control ordinance (normally, in California, this would be a county's responsibility). The County of Santa Cruz, for example, has ordinances which makes a dog owner responsible for a dog's habitual barking and another for a dog's threatening behavior.
6.12.090 Noisy animals.
A. It is unlawful for any person to keep or harbor any dog, cat or other animal, whether licensed or not, which by habitual howling, yelping, barking or other noise unreasonably disturbs or annoys any person with ordinary sensitivities. When determining if there has been a violation of this section, the use and character of the property where the animal is located as well as the neighboring properties shall be taken into consideration.
6.12.100 Harassment, threat or injury by animals.
It is unlawful for the owner of any animal to suffer or permit the same to annoy and harass, chase, threaten to inflict or inflict injury of any kind on any person. (Ord. 4490 § 6, 1998: prior code § 8.05.410: Ord. 2170, 8/19/75)
In looking at these statutes, it is important to notice particular phrases, such as "unreasonably disturbs or annoys" and "person with ordinary sensitivities". It is up to the animal control officers to determine whether the dog and/or owner violate any such ordinance. Usually, ordinances of this type authorize the animal control officer to impound the dog(s) and, if sufficiently violent and not able to be rehabilitated, then to put the dog(s) to sleep.
If your county has such an ordinance, you might choose to file a report about your neighbor's dogs. In their investigation, the animal control officers could observe the behavior you are talking about and can issue orders to control the animals to protect your parents from the behavior found to be annoying, harassing, or potentially dangerous.
If one or more of the dogs actually gets into your yard and injures you or one of your cats, you can pursue other steps, including a Small Claims or other civil lawsuit, to recover compensation for the damage caused by that conduct.
Your parents might be able to sue their neighbors for an order forcing them to abate (end or minimize) the dogs' behavior and for compensation, under the theory that the conduct of the neighbor's dogs is a "private nuisance" which interferes with your parents' use of their land. Nuisance is defined in California Civil Code section 3479. They can file an action in the Small Claims Court to obtain these remedies.
Another issue is what seems to be your mention of damage to the fence between your property. If the fence is a common fence, on the property line, each of you owns it and each of you has the right to recover the costs of repair for damage caused to the fence by anyone. If the fence is solely on your neighbor's side of the property line (not shared) then you would not be able to force him to pay you the cost of repairing the fence.
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Answered on Aug 19th, 2011 at 1:37 PM