Since limited liability companies can be a pass-through entity, owners are taxed on their personal income. S-Corp shareholders are taxed personally. The S-Corp, however, is not. C-Corp income is taxed at the corporate level first, then again at the personal level. This is called "double taxation." Non-Profits are only taxed once and can write off most of their expenses. Sole Proprietors are taxed only on their personal tax return.
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
LLP, Limited Liability Partnership: a partnership where a partner's liability for the debts of the partnership is limited except in the case of liability for acts of professional negligence or malpractice. In some states, LLPs may only be formed for purposes of practicing a licensed profession, typically attorneys, accountants and architects. This is often the only form of limited partnership allowed for law firms (as opposed to general partnerships).
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.