If the arrest was recent
Start with the county jail
Connecticut has no county jails.
After an arrest, a person who is not released is held in a Connecticut DOC correctional center as a pretrial detainee, so the SAME DOC Inmate Information Search locates them once they are booked into DOC.
Someone arrested very recently may still be at a municipal police or State Police lockup before transfer; if the DOC search shows nothing yet, contact the arresting police department.
Not applicable in Connecticut. There are no county sheriff jails or county jail rosters; all detention, pretrial and sentenced, is run by the state DOC and searchable through the one DOC tool or VINELink.