Conn. Gen. Stat. § 46b-115t: Appearance of parties and child.

(a) In a child custody proceeding in this state, the court may order a party to the proceeding who is in this state to appear before the court in person with or without the child. The court may order any person who is in this state and who has physical custody or control of the child to appear in person with the child.

(b) If the court orders the appearance of a party who is outside this state, the court may order that a notice is given in accordance with section 46b-115g and that such notice include a statement directing the party to appear in person with or without the child and informing the party that failure to appear may result in a decision adverse to such party.

(c) The court may enter any orders necessary to ensure the safety of the child or of any person ordered to appear pursuant to this section.

(d) The court may order a party to pay for reasonable and necessary travel and expenses of a party to the child custody proceeding or the child who is outside the state.