If she reported her cat's death under the circumstances you describe, then the police would be investigating a case of some dangerous lunatic breaking and entering, vandalizing, and animal cruelty.
Animals are property under law, so if someone kills your animal they only have to reimburse you the monetary value of the animal. The only exception are service animals (like a seizure alert animal, seeing eye dog, police dog, bomb sniffing dog, etc.) Harming/killing a service animal is a felony in most states.
As for the rumors, that's pretty reasonable regardless of what the police think. If she's kind of an outsider in the town, and especially if people were already saying weird things about her. It could just start with the neighbors seeing a bunch of cops descend on her home and roll from there.