Responsibility is about the company, not the paperwork. Owners look at experience, finances, licenses, bonding, safety and past performance.
Before award, a public owner may ask the apparent low bidder for references and a list of similar projects. Some owners also ask for financial statements.
Keep your project list, references and license records current. A slow answer to an owner's request can cost you the award.
Each owner and state defines the test in its own way. Read the bid documents for the criteria that apply.