Limited liability companies can claim deductions but not tax-exempt status. S-Corps can claim deductions but not tax-exempt status. C-Corporations are not tax-exempt entities Not only are donations to Non-Profits tax-exempt, but NPOs can themselves apply for tax-exempt status. Sole Proprietorships are the least official business entity and cannot claim tax exemption.
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.