File with the appropriate federal, state, and local governmental agencies. Depending on the business purpose of your LLC and the jurisdiction in which you organize, you may have to file additional forms relating to LLCs with certain governmental agencies. Each industry is regulated differently—as is each local jurisdiction—and so it is best to ask an attorney or accountant for assistance in this matter.
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.