Only the Cat by Marian Babson
Now, smiling weakly, suffering from severe bruising and a head injury which had left her with complete amnesia about the accident, the events leading up to it, and even the people surrounding her, here she was, back in their midst. Or was she? While the real Vanessa lay in a coma, her devoted twin, devastated by news of the accident, decided to take her place in the self-absorbed retinue surrounding the reclusive millionaire who maintained Vanessa and the rest of them. But had it been an accident - or was it attempted murder? Vance had to find out. Yet while pretending amnesia was an effective cover, it was also a double-edged sword. Vance was suddenly besieged by people all eager to supply ready-made memories: the unsavoury roue who claimed to be her lover; the sinister women who avowed to be her best friends; and finally the sinister observers who kept their silence - but constantly watched, waiting for Vance to put one foot wrong. But Vance could handle those. There was only one real problem: Gloriana, Vanessa's beautiful white Angora cat who regarded her new mistress with a dark suspicion bordering on hostility. If the cat couldn't be won over, then the whole charade was in danger of being exposed.