Will I be liable for unpaid CT tax of prior business owner?

You state that there are unpaid taxes of the prior business owner.  If that is acccurate, you would probably not be liable for his/her taxes (although you should be careful if you are buying any assets from this person, as it is possible that tax liens have attached to the assets; although you would not technically owe any taxes, you would be buying the assets subject to the liens, and the taxing authority could foreclose).  However, I'm not sure it is accurate.  Are you sure that the taxes are owed by the person from whom you're buying the business and not the business itself?  There is a big difference and if, for example, you are buying a corporation or llc which owes taxes, that entity would still owe the taxes even under new ownership.  Also, even if you are not buying the business entity, but only the assets of the business entity, if you continue on with the same business (same customers, same products/services, same location, etc.) there could theoretically be successor liability for the taxes.