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Countess Heidi Scarlioni was the wife of Count Carlos Scarlioni who, unbeknownst to her, was a Jagaroth.
Heidi met Carlos Scarlioni whilst working for her father in a Swiss bank. She often found herself bored with clients, but Scarlioni caught her eye as his paperwork was immaculate, which she found to be unusual considering how old the family vault was. Intrigued with this mysterious character, she eventually married him. (City of Death)
The Countess assisted Scarlioni in making preparations to steal the Mona Lisa, even going to the Louvre wearing a micromeson scanner to test its defences. However, while carrying this out, the scanner was stolen bythe Fourth Doctor, an act she promptly reported to her husband, resulting in the arrest of both The Doctor and Romana II.
The Countess was killed by her husband shortly after he revealed his true alien origin to her, although he deeply regretted her death. (City of Death)
BEHIND THE SCENES
Her first name is only revealed in the novelisation
Her character is greatly expanded upon in the novelisation, providing a backstory and greater details of her relationships. For instance, she is shown to take a particular dislike to Romana after the Count spends some time with her, and is shown to be very dear to the Count himself.. (City of Death)