LLC members are not personally responsible for the company's debt or liability. S-Corp shareholders are not personally responsible for the company's debt or liability. C-Corp shareholders are not personally responsible for the company's debt or liability. Non-Profit directors are not personally responsible for organizational debt or liability. Sole Proprietors are personally responsible for debt and liability.
While limited liability companies have less compliance requirements than other entity types, there are reports and licenses that need to be filed and maintained. S-Corps usually will need to file reports and pay compliance fees on an annual or semi-annual basis. C-Corps generally must file reports with their state, as well as a host of other regulatory and compliance fees. Non-Profits have more compliance responsibilities than other entities as they must continually preserve their tax-exempt status. Sole Proprietors do not have ongoing compliance fees.
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.