Connecticut Summons in a Third-Party Complaint is a court process used to bring a third party into a case between two other parties. It is a type of legal document that is served on a third party to give them notice of the lawsuit and to require them to appear in court to answer the claims made against them. There are two types of Connecticut Summons in a Third-Party Complaint: Original Summons and Alias Summons. An Original Summons is the initial court document served on a third party to bring them into the case. An Alias Summons is a second document that is served on the same third party if they fail to appear in court or respond to the Original Summons.