For federal tax purposes, the Internal Revenue Service has separate entity classification rules. Under the tax rules, an entity may be classified as a corporation, a partnership, a cooperative or a disregarded entity. A corporation may be taxed as either a C corporation or elect to be treated as a Subchapter S corporation. A disregarded entity has one owner (or a married couple as owner) that is not recognized for tax purposes as an entity separate from its owner. Types of disregarded entities include single-member LLCs; qualified sub-chapter S subsidiaries and qualified real estate investment trust subsidiaries. A disregarded entity's transparent tax status does not affect its status under state law. For example, for federal tax purposes, a sole-member LLC (SMLLC) is disregarded, so that all its assets and liabilities are treated as owned by its single member. But under state law, an SMLLC can contract in its own name and its owner is generally not personally liable for the debts and obligations of the entity. To be recognized as a Cooperative for tax purposes Cooperatives must follow certain rules under Sub Chapter T of the Internal Revenue Code.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.