That depends. If you are an at-will employee and say something personal about how he or she really gets your goat, then you can be fired. However, if you make a complaint of public concern, such as, “My boss makes me violate the law,” you may be protected by the First Amendment and Connecticut law. Finally, if your complaint involves the terms and conditions of your employment and seeks to involve other employees, you may be protected by the National Labor Relations Act.
Read more on Attorney Hayber’s blog- https://ctemployeerightsblog.wordpress.com/.