If the LLC will be Manager governed, an elected set of Managers (who can be people other than Members), will make the business decisions. Under this structure, the business will more closely resemble a traditional corporation, with the Managers acting as directors, and the owners acting as shareholders. If an LLC elects to be governed by Managers, this decision must be stated in the Articles of Organization.
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.