Connecticut's counterpart to the United States Congressional Research Service is the Office of Legislative Research. Like the CRS, the OLR is a non-partisan research service.
The reports on the OLR website are a potential source for Connecticut legislative history. Remember, the Assembly asked the OLR to prepare these reports so it is at least possible that the Assembly read them and had them in mind when enacting legislation. The OLR deals with Reports in distinct ways:
OLR posts recent reports here. Right now, the reports for September are available. These include, inter alia, newly issued reports on Strict Liability, Boater's Liability Insurance and more. Selected past reports are here. Right now, these include reports from August. "Backgrounder" reports are here. These are reports that cover issues of long term interest.
Reports are searchable by topic and there is an archive of past reports and other documents generated by the OLR. Finally, you can search the reports by full-text here.
Next time you are trying to decide what the Connecticut Assembly had in mind when it passed a new law, see if there is an OLR report that can help you.