In the case of any application for the appointment of a conservator of the estate, as said terms are defined in § 45a-644, and, in the case of any application for involuntary representation, as defined in subsection (d) of § 45a-644, the application shall state that the respondent, as defined in subsection (e) of § 45a-644, either is or is not, receiving such aid or care from the state, whichever is true, and a copy of each application which states the respondent is receiving such aid or care shall be sent by the court to the Commissioner of Administrative Services, in accordance with the provisions of subsection (a) of § 45a-649 or § 45a-646, as the case may be.