In general, a person has to have lost their competence for a Court to appoint a Conservator against their will. In some states it is called a Guardian in a Guardianship proceeding.
In Connecticut, “competent” means the person must have the mental capacity sufficient to comprehend the nature, extent and consequence of the transfers.
Specifically, the Connecticut Statute Says
(c) “Incapable of caring for one’s self” or “incapable of caring for himself or herself” means that a person has a mental, emotional or physical condition that results in such person being unable to receive and evaluate information or make or communicate decisions to such an extent that the person is unable, even with appropriate assistance, to meet essential requirements for personal needs.
(d) “Incapable of managing his or her affairs” means that a person has a mental, emotional or physical condition that results in such person being unable to receive and evaluate information or make or communicate decisions to such an extent that the person is unable, even with appropriate assistance, to perform the functions inherent in managing his or her affairs, and the person has property that will be wasted or dissipated unless adequate property management is provided, or that funds are needed for the support, care or welfare of the person or those entitled to be supported by the person and that the person is unable to take the necessary steps to obtain or provide funds needed for the support, care or welfare of the person or those entitled to be supported by the person. CGS §45a-644
New York has similar rules and definitions.