My state refund has not been processed by the State of Connecticut. My federal refund received. How can I know about my state refund now?

If your return was accepted, only the State knows when you will receive your refund.  Click on the following link, you can check your Connecticut refund there.

https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-connecticut-tax-refund/00/26564