Legal Question in Family Law in Connecticut

In CT, everything is a marital asset and thus divisible in a divorce. Usually, things you brought to the marriage, or things inherited or gifted to you during the marriage, stay yours. So, in your case, if you had the business before the marriage then the value of the business at the time of the marriage would stay yours, but the appreciation in value during the marriage would most likely be divided. Of course, she wouldn't necessarily get (or probably want) "half the business". You could swap the value of half the business against, say, equity in the house or a 401K or some other asset.