You will find that in almost every state of the USA and in most Western countries it is illegal to abandon your cat for the simple reason that it is cruel. All countries in the West and all states in America have animal welfare laws which protect cats from abuse and cruelty. The obstacle to prosecution is evidence.
Sometimes there is specific reference to the abandonment of cats in statutes. For example, in the animal welfare statutes of California, Arizona and Arkansas there are references to the abandonment of animals making it a criminal act.
If the laws of a US state or a country does not specifically refer to the abandonment of a cat as a crime it should be argued that it is still a crime under a different heading within the statute. For example, the statue might refer to the mistreatment of an animal or causing unnecessary physical suffering to any animal due to neglect. These are general headings which should arguably encompass abandonment.
There is no question that abandoning a cat is being cruel to the cat. Clearly it depends where it happens. Some people think that they can abandon their cat in woods and the cat will be alright. This is clearly a fallacy. Fully domesticated cats don’t do well free of human care. Sometimes people abandon cats outside the front door a cat rescue center. They put the cat in a box and it might be in the middle of winter. The cats are in the box all night in freezing conditions. This is obviously cruel.
There are occasions when it might not be deemed to be cruel to abandon a cat and in which case it might not be a crime if the word abandonment is not specifically used in the law. Example, if a person abandoned a cat in a box outside a rescue center during the daytime and left a clear note on the box stating what she was doing. It is likely that the box would be spotted and the cat taken into the shelter quickly. Suffering would be avoided probably. But why do this when the rescue center reception is 30 feet away?
The key issue is that abandonment will almost certainly cause suffering and pain. The owner is causing pain to their cat. This is cat abuse and it must fall under all animal welfare laws no matter where you live.
In conclusion, therefore, if you ask the question “is abandoning a cat illegal?” the answer must be, Yes, unless there are specific circumstances which means that the cat did not suffer physically or psychologically.
Finally, abandoning a cat is careless and lazy. If a person wants to divest themselves of their cat for whatever reason it doesn’t take a lot of effort to ensure that the cat goes to a good home either via a rescue center or through personal connections and friends. A little bit of effort will avoid a potentially criminal act.
The fact that cat abandonment is a crime does not necessarily mean that it leads to a successful prosecution for the obvious reason that there will usually be no evidence because it is done surreptitiously at night. On occasions when there is evidence it is because there are surveillance cameras.
P.S. Sometimes we have to forgive people who abandon cats provided they are not cruel to their cat.