Leona Helmsley's recent death caused quite a stir in the news when she, in her will, bequeathed almost $12M to be held in trust for the care of her dog, Trouble. The New York Surrogate's Court eventually knocked that amount down to $2M- notwithstanding the testimony of Trouble's $60,000/year guardian.
A lot of press was generated concerning "Pet Trusts". Approximately 40 states have either adopted uniform laws or enacted their own legislation enabling their citizens to create such trusts. The Connecticut legislature considered one proposed law in 2005, SB1191: An Act Concerning the Creation of Trusts for the Care of Domestic Animals. That bill appears to have died somewhere in the Judiciary Committee and has yet to be reconsidered.
Until then, consider the following:
1. Specifically bequeath in your will your pet to a friend of family member along with some money for its care.
2. Specifically bequeath in your will a dollar amount to a person, with the condition that it be spent for the care of your pet.