I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney client relationship.
Yup, have the cat destroyed. Contact the proper authorities and they will institute proceedings to have this poor excuse of a tamed animal put to sleep. Also, you get to sue the dog owner for the cost of the cat and if the judge is really sympathetic, punitive damages for your emotional distress. but usually, you can only recover cost of animal --> our legal system in the area of animal rights is lacking.
Here are some washington state laws:
RCW 16.08.030
Marauding dog -- Duty of owner to kill.
It shall be the duty of any person owning or keeping any dog or dogs which shall be found killing any domestic animal to kill such dog or dogs within forty-eight hours after being notified of that fact, and any person failing or neglecting to comply with the provisions of this section shall be deemed guilty of a misdemeanor, and it shall be the duty of the sheriff or any deputy sheriff to kill any dog found running at large (after the first day of August of any year and before the first day of March in the following year) without a metal identification tag.
RCW 16.08.070
Dangerous dogs -- Definitions.
Unless the context clearly requires otherwise, the definitions in this section apply throughout RCW 16.08.070 through 16.08.100.
(1) "Potentially dangerous dog" means any dog that when unprovoked: (a) Inflicts bites on a human or a domestic animal either on public or private property, or (b) chases or approaches a person upon the streets, sidewalks, or any public grounds in a menacing fashion or apparent attitude of attack, or any dog with a known propensity, tendency, or disposition to attack unprovoked, to cause injury, or to cause injury or otherwise to threaten the safety of humans or domestic animals.
(2) "Dangerous dog" means any dog that according to the records of the appropriate authority, (a) has inflicted severe injury on a human being without provocation on public or private property, (b) has killed a domestic animal without provocation while off the owner's property, or (c) has been previously found to be potentially dangerous, the owner having received notice of such and the dog again aggressively bites, attacks, or endangers the safety of humans or domestic animals.
(3) "Severe injury" means any physical injury that results in broken bones or disfiguring lacerations requiring multiple sutures or cosmetic surgery.
(4) "Proper enclosure of a dangerous dog" means, while on the owner's property, a dangerous dog shall be securely confined indoors or in a securely enclosed and locked pen or structure, suitable to prevent the entry of young children and designed to prevent the animal from escaping. Such pen or structure shall have secure sides and a secure top, and shall also provide protection from the elements for the dog.
(5) "Animal control authority" means an entity acting alone or in concert with other local governmental units for enforcement of the animal control laws of the city, county, and state and the shelter and welfare of animals.
(6) "Animal control officer" means any individual employed, contracted with, or appointed by the animal control authority for the purpose of aiding in the enforcement of this chapter or any other law or ordinance relating to the licensure of animals, control of animals, or seizure and impoundment of animals, and includes any state or local law enforcement officer or other employee whose duties in whole or in part include assignments that involve the seizure and impoundment of any animal.
(7) "Owner" means any person, firm, corporation, organization, or department possessing, harboring, keeping, having an interest in, or having control or custody of an animal.
[1987 c 94 § 1.]
NOTES:
Severability -- 1987 c 94: "If any provision of this act or its application to any person or circumstance is held invalid, the remainder of the act or the application of the provision to other persons or circumstances is not affected." [1987 c 94 § 6.]
RCW 16.08.090
Dangerous dogs -- Requirements for restraint -- Potentially dangerous dogs -- Dogs not declared dangerous.
(1) It is unlawful for an owner of a dangerous dog to permit the dog to be outside the proper enclosure unless the dog is muzzled and restrained by a substantial chain or leash and under physical restraint of a responsible person. The muzzle shall be made in a manner that will not cause injury to the dog or interfere with its vision or respiration but shall prevent it from biting any person or animal.
(2) Potentially dangerous dogs shall be regulated only by local, municipal, and county ordinances. Nothing in this section limits restrictions local jurisdictions may place on owners of potentially dangerous dogs.
(3) Dogs shall not be declared dangerous if the threat, injury, or damage was sustained by a person who, at the time, was committing a wilful trespass or other tort upon the premises occupied by the owner of the dog, or was tormenting, abusing, or assaulting the dog or has, in the past, been observed or reported to have tormented, abused, or assaulted the dog or was committing or attempting to commit a crime.
[1987 c 94 § 3.]
NOTES:
Severability -- 1987 c 94: See note following RCW 16.08.070.
RCW 16.04.015
Damages, liability.
Except as provided under RCW 16.04.100, whenever any animals trespass as provided in RCW 16.04.010, the owner or person having possession of such animal shall be liable for all damages the owner or occupant may sustain by reason of such trespass.
RCW 16.04.030
Actions for damages.
If the owner or person having such animals in charge fails or refuses to pay the damages done by such animals, and the costs, or give satisfactory security for the same within twenty-four hours from the time the notice was served, if served personally, or in case of horses, mares, mules and asses, within twenty-four hours from the time such notice was posted, if served by posting the same, and in case of cattle, goats, sheep and swine within ten days from the time of such posting, the person damaged may commence a suit, before any court having jurisdiction thereof, against the owner of such animals, or against the persons having the same in charge, or possession, when the trespass was committed, if known; and if unknown the defendant shall be designated as John Doe, and the proceedings shall be the same in all respects as in other civil actions, except as modified in RCW 16.04.010 through 16.04.070. If such suit is commenced in superior court the summons shall require the defendant to appear within five days from the date of service of such summons, if served personally.