In New England, town governments have always been relatively strong, and county governments relatively weak. Traditionally New England counties only provided courts, jails, and sheriffs. They did not provide the kind of services seen in other parts of the country, such as county roads, general government services for unincorporated areas, etc.
Connecticut now has judicial districts, which provide the courts that formerly were provided by counties. The judicial district boundaries are similar to the old county boundaries.
Added:In Connecticut and Vermont, property taxes and zoning are administered by cities and towns. Construction-related inspections tend to be done by larger cities and towns, while the state handles the smaller cities and towns.