Could it be correct to assume that the animals present in this story reflect human violence and madness in the story "The Black Cat"?

There are two elements to consider in this question about "The Black Cat." When interpreting a literary work, one draws on the information that the author presents. This information enables one to form an argument or thesis statement which can then be supported with further evidence from the text. An "argument" is different from an "assumption" as the latter is based on ideas that the reader had before reading the text. Because an assumption stems from the reader's ideas, it cannot be evaluated as correct or incorrect. An argument's validity can be weighed based on the support present in the text.
In Edgar Allan Poe's story, the narrator associates both cats with his wife, who was a cat lover. He kills the first cat, Pluto, an act that foreshadows his later killing his wife. He associates the second cat with Pluto, which it resembles. His idea that the shape marked by the different color fur is changing is not rational, and his association of the shape with the gallows indicates his guilt over killing his wife.
In this respect, both cats are associated with death, and the narrator's ideas and actions are irrational. Killing an animal or a human being is definitely violent behavior. The concept of "madness," which frequently occurs in nineteenth-century literature, can be understood as indicating a number of kinds of mental illness. The narrator's actions do not seem to indicate good mental health, so it is likely that the author was indicating that he was, or soon would be, "mad."