Without an appearance, it is only a matter of time before the opposition files a "Motion for Default for Failure to Appear". After that the Moving party can later make a Motion for Default Judgment. You should file a pro se Appearance and also seek the counsel of an attorney.
I am assuming you are in civil court. If you do not appear then a default will be entered against you. That will allow the Plaintiff's to obtain a judgment against you without you having the opportunity to defend yourself. That monetary judgment can then be enforced against you and your assets or your pay. You really should appear and defend yourselves, especially if you think you are in the right. Failing to appear may deprive you of your right to ever contest this suit including to size of the monetary award.
The appearance is only a form that tells the court who you are and where and how to contact you. You will next need to file a response to the complaint against you. There are a couple of options available to you. You can file a request to revise the complaint, a motion to strike the complaint or an answer. You must consider them in that order too. Once you progress past an option you cannot go back to it. It is difficult to advise you beyond filing an appearance without knowing more facts of your case and the specifics of the complaint filed against you and how it was served. You should also know, that you only have 10 days after you appear to contest personal jurisdiction via a motion to dismiss.
While the other advice is just fine, step one should be to turn the complaint over to your insurance agent. Such claims are generally covered under a homeowners or renters policy. Even if it was an intentional act for the child, it wasn't as to you. Also note that CT has a statute creating parental liability for acts of children.
As the 3 Litchfield question posts appear to concern the same case / person see my consolidated answer at ( http://www.avvo.com/legal-answers/what-is-a-claim-for-jury-form---i-plan-on-represen-386410.html?answered=true )
Disclaimer: The foregoing answer does not constitute legal advice, is provided for informational and educational purposes only for persons interested in the subject matter. Each situation is fact specific and may be subject to state specific laws. Without a comprehensive consultation and review of all the facts and documents at issue it is impossible to evaluate a legal problem fully. This answer does not create an attorney-client relationship.