John, What kind of court records are you talking about?
Yes, probate records can be quite useful--if your ancestors owned property. I thought maybe you meant civil or superior court. The probate system in Conn. is a bit confusing since it is based probate districts which generally track with towns. That is, they are not organized on the county level. Over the centuries new districts have been created so it is important to follow the establishment of new towns and probate districts in order to know where to look for records for the person of interest.