I agree with @TomD8 , since you do not physically work in CT, you usually would not be subject to CT tax.
You say " The company does withhold Connecticut taxes". This means, you will have to file a CT non-resident return to get a refund. That's when it may all come to a head with CDRS. Your employer must have some reason for withholding CT tax.
In particular, "attend....state court appearances, etc, through my work computer" sounds pretty iffy. You may become the test case for this situation.
