I really like Marian Babson's mysteries, but The Cat Next Door is not one of her good ones. There isn't much of a mystery, and the solving of it depends on coincidence and confession, not investigation.
Margot--and she doesn't seem to have a last name--is a photographer who's returned to her family home in England after several years working in New York City. She's come home because her Aunt Chloe is about to go on trial for killing her Aunt Claudia--Chloe's twin sister--and the family wants to show solidarity.
Everyone in the unnamed family is neurotic, which can be amusing in a cozy mystery but which doesn't work in this case. The characters are defined and limited by their neuroses: the teenager who refuses to leave her bed after witnessing the murder, the uncle who does nothing but eat compulsively, the aunt who's buried herself in reading Regency romances rather than face the family scandal of murder. Even Margot, the main character, suffers from Chronic Fatigue Syndrome--which is coyly not named until the very end of the book, as if it too were a mystery--which makes her a particularly unlively sleuth. Not that any sleuthing gets done in the book. Stuff just happens, and Margot thinks for a few minutes and decides in the next-to-last chapter that Someone Else killed her aunt, not Chloe. She's wrong about who the murderer is, but fortunately the real murderer confesses.
It's a thoroughly unsatisfying book. For a murder mystery, that's unforgivable.