In any matter before a Probate Court in which the capacity of a party to the action is at issue, the court may order an examination of the allegedly incapable party by a physician or psychiatrist or, where appropriate, a psychologist, licensed to practice in the state, except that a conserved person, as defined in section 45a-644, the respondent to an application for involuntary representation made under section 45a-648 or a respondent to a petition for appointment of a temporary conservator made under section 45a-654 may refuse to undergo an examination ordered by the court under this section. The expense of such examination may be charged against the petitioner, the respondent, the party who requested such examination or the estate of the allegedly incapable party in such proportion as the judge of the court determines. If any such party is unable to pay such expense and files an affidavit with the court demonstrating the inability to pay, the reasonable compensation shall be established by, and paid from funds appropriated to, the Judicial Department, except that if funds have not been included in the budget of the Judicial Department for such purposes, such compensation shall be established by the Probate Court Administrator and paid from the Probate Court Administration Fund.