Filing a limited liability company separates your personal assets from those of your business. This prevents you from being financially responsible for debts and liabilities of your business. Even though members are still liable, that liability is limited to the extent of their investments in the business. If, for instance, your company is involved in a lawsuit, the assets of the LLC itself could be in jeopardy, while the personal assets of the members/owners would be protected.
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.