Connecticut statutes determine how a marriage can be terminated. Under C.G.S. sec 46b-40 (a), a marriage is dissolved only by (1) the death of one of the parties or (2) a decree of annulment or dissolution of the marriage by a court of competent jurisdiction. In the "olden days," a party had to allege and prove fault such as adultery or willful desertion in order to be granted a divorce.
Now a party can simply allege and prove that the marriage has "broken down irretrievably" in order to be granted a divorce. This is referred to as a no-fault divorce. If a party would like to allege fault in the complaint, he/she is free to do so but it is not required. Most often, a party simply states that the marriage has broken down irretrievably.
Even though fault does not have to be alleged in the complaint, it can become a major factor in determining the various aspects of a divorce such as alimony and property division. Another way to view it is that fault can become a part of a divorce case through the backdoor. It is not needed to start and obtain a divorce, but it is often considered when determining the financial matters such as alimony and the division of assets.