There is no Indian Consulate in Connecticut!
Since Connecticut comes under the jurisdiction of Consulate at New York, the nearest Indian Consulate you should visit is located at New York at the below address
New York Consulate Address
Consulate General of India,
3 East 64th Street
(Between 5th and Madison Avenues)
New York, NY 10065
Helpline Tel: 347-721-9276