Is anyone else in CT waiting weeks for their return to be accepted (after it has been approved) 4 days to be approved... Now it's been 8 more - and still isn't accepted?

You seem to be confused about the words "accepted" and "approved."

 

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

 

 

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.

 

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

 

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

 

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573