Even if you do not have legal immigration status you can renew your Connecticut driver’s license. (You cannot get a license for the first time if you are out of status, however.) Just go to DMV when your license is expiring and ask for a regular license. Do not ask for the new Connecticut Select license. If you are illegal and ask for a regular license renewal you will get it. If you ask for the Connecticut Select license you will end up with no license!
The Connecticut Select license is a higher-security license that will be used to enter federal office buildings and board planes. It requires proof of legal status. so if you are not in lawful status, don’t ask for it. In addition, use common sense: if you have a final order of removal but were not deported and did not leave the U.S., you should not be going to DMV looking for a license. You are not supposed to be in the U.S, and are likely to be taken away by ICE if you ask for a license.
But for someone whose only problem is lack of a lawful immigration status, and who obtained a license in the past, it is possible to renew your Connecticut license. Just be sure to ask for a regular license, not a Connecticut Select license.