Sometimes. The person must hold both recorded legal title by being a trustee or co-trustee and a sufficient beneficial interest in the domicile through the trust to be considered an owner for exemption purposes. A person who is not a trustee does not have legal title and does not qualify for a personal exemption.
A trustee or co-trustee has the necessary beneficial interest if he/she is a named beneficiary in a recorded certificate of trust, declaration of trust or trust schedule of beneficiaries, has an express right to occupy the property under the trust or is in fact occupying it as his/her domicile, or has rights under the trust that indicate he/she can occupy the property and no one else has a beneficial interest that is exclusive or inconsistent with that occupancy. For instance to direct the trustee to turn over the title or use of the property, to receive proceeds from the sale or rental of the property or to use, apply, or spend any trust assets during his/her lifetime.