The connection principle leads to a dilemma:

Either, the connection principle is a claim about access consciousness,

In which case, any mental state to be a mental state, must be capable of being reported and reasoned about. In this case, the connection principle is obviously false, because one might have a conscious state but not be able to report it—eg because one's mouth is taped shut.

Or, the connection principle is a claim about phenomenal consciousness,

In which case, any mental state must in principle have an associated feeling. But whether or not every human thought has an accompanying feeling is an unsettled empirical issue for which philosophical reflection is unhelpful.

In either case, the connection principle should be rejected.

Access consciousness: mental states that are available from reporting and reasoning.

Phenomenal consciousness: a mental state that has a certain feeling associated with it.

Ned Block (1990).