In a word "No." There is nothing in Connecticut law which uses the term "permanent alimony." Alimony, regardless of the form it takes, is simply referred to as "alimony." Almost all alimony orders terminate on the death of either party or the remarriage of the recipient. This is commonly referred to as open-ended alimony because it has no specific end date. Almost all alimony orders issued a court are subject to modification in the event of a substantial change in circumstances or if the payor proves that the recipient is living with another person under circumstances which reduce his or her needs (sometimes called "cohabitation"). It is common for alimony orders to end on a specified date if alimony has not terminated earlier, but there is no specific term for this in Connecticut law.
Connecticut General Statute Section 46b-82 provides the courts with authority to award alimony. In deciding whether to award alimony, the statute requires a court to consider the following factors in determining the duration and amount of the alimony award: the length of the marriage, the causes for the annulment, dissolution of the marriage or legal separation, the age, health, station, occupation, amount and sources of income, vocational skills, employability, estate and needs of each of the parties, property distribution award, and if the parties have minor children, the desirability of such parent's securing employment. The statute makes no explicit reference to the term permanent alimony.
In Connecticut, open-ended alimony awards are fairly uncommon. The statute was recently amended to require a court awarding open-ended alimony to state with specificity its reasons for making this award. Once the court issues an alimony award, the parties may request modification or termination of that award upon a showing of a substantial change in circumstances pursuant to Connecticut General Statute Section 46b-86.
Nationwide, many states have recently considered whether to eliminate "permanent alimony." In Connecticut, legislation introduced in the 2014 session purported to make it easier to modify or terminate alimony when the paying spouse wants to retire or when the recipient spouse cohabitates with another person. The bill failed to pass at the end of the session.