Generally speaking, the very purpose of creating an entity with limited liability protection (such as that which an LLC affords) is to protect the business owners from being held personally liable for the debts of the business. BUT, in many states, there are exceptions to this basic premise and key among them is where a business collects sales taxes (which rightfully belong to the state) but then fails to turn the collections over to the state as required. In those cases, a state may potentially pursue those who it deems responsible (executive officers of corporations and the owners of LLC's) for the unpaid sales taxes. I offer this observation based on general legal principles and without knowing whether the same holds true in the state of Connecticut.
I would strongly advise you to consult either or both bankruptcy counsel and an attorney who specializes in defending tax claims against business owners.
Disclaimer: The answer to your question does not create an attorney-client relationship, and is for informational purposes only. You should consult your attorney for legal advice tailored to your individual circumstances. The answer is not, nor is it intended to be, legal advice.
Mr. Stansell's concerns are valid. In most states sales taxes and employment taxes can be collected from "responsible persons." This may or may not include all members of the LLC. But it could include non-owner officers and employees like the CFO.