Vermont "corporation", "incorporated", "company", or "limited", or the abbreviation "corp.", "inc.", "co.", or "ltd.", or words or abbreviations of like import in another language; shall not have the word "cooperative" or any abbreviation thereof as part of its name unless the corporation is a worker cooperative corporation Title 11A, § 4.01 Vermont Statutes
A partnership is a business relationship entered into by a formal agreement between two or more persons or corporations carrying on a business in common. The capital for a partnership is provided by the partners who are liable for the total debts of the firms and who share the profits and losses of the business concern according to the terms of the partnership agreement.
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.