I searched online to find some information on this for you. It appears that in Connecticut, judges, retired judges, Connecticut state referees, Connecticut justices of the peace, and ordained or licensed clergymen (belonging to any state) may perform weddings in Connecticut. If you wish for a friend or family member to get ordained online and perform the ceremony, the marriage may not be recognized legally. You may need an authorized officiator is present to confirm your marriage ceremony and to sign your marriage license.
I would recommend reaching out to your country clerk to get more information on this and confirm what you need to do.