Connecticut has a lot of things going for it, depending on what's important to you when it comes to a place to live. It also used to have the most rich people anywhere else in the country, but that isn't helping it much now when it comes to convincing people to stay. The state is suffering from a lot of income inequality, and there just aren't enough high-paying jobs for everyone.
The state is also losing a lot of seniors who can't afford to retire there or who want somewhere with milder winters. Both factors have caused it to lose population in recent years.