The court in CT is where it happened, therefore they are the court of jurisdiction, the hard part you will have is serving her (due process) as to do that you must know where she is, unless you petition to serve her via publication in her last known area (CT...HOWEVER, you have the obligation of due diligence too, therefore because YOU know she moved to Kansas, you are going to have to find her in order to serve her)
Service by sheriff is less costly than using a process server usually, and you need to look up your local laws in your state in regards to actual service (generally, the prefered method is physical service, in most jurisdictions you can serve via certified mail, however you usually have to petition for that, and the third option (generally) is service by publication (putting an ad in the local newspaper, stating whom is suing whom, when the hearing date is, etc but this also must be petitioned for in most jurisdictions)
Good luck