If the business is owned solely by one person, only that person needs to sign. If it is a partnership of two or more people (but not a formal legal entity), both or all of the "partners" must sign. If it is a legal partnership, any officer who has authority to sign on behalf of the partnership may do so. If it is a corporation, an officer who has signatory authority must sign - which is usually the President, but not always.
All signatures must be made in front of a notary, the Town Clerk, or the Assistant Town Clerk. Do not sign the certificate unless it is in front of one of these three individuals. An individual must be 18 years of age or older to legally sign a business certificate.