As the State of Connecticut only issues licenses and permits and not identification cards and further does not require one to carry identification... No.
However and on a state-by-state basis, one may be accused of obstruction if one does not identify oneself (note, Not 'produce' identification') if:
- They are a SUSPECT. That is, the officer has reasonable suspicion the person has committed or is about to commit a crime.
- They are a WITNESS The officer has good reasons to believe the person’s identification is important to leading to credible evidence in an investigation.
- They fail to provide their name during BOOKING