Through self discovery-found an error on CTR-entered incorrect state for ID. We have made the correction and notified FinCen.
Do we also contact our regulator, noting the correction?

No need. Document the error, that you identified it, checked to see if it resulted from a missing or inadequate control, and that you filed the amending CTR.

No - that would be overkill IMHO. The regulator would be more interested in whether you have adequate internal controls to prevent CTR error occurrence. As you have identified an error, I would consider whether those controls could be strengthened.

We have very limited occurrences with corrections-this one slipped past and was corrected within a short period of time. No issues in the past with our CTR filing program from a regulatory or third party reviews.
According to the BSA E- Filing Helpdesk, Instructions for Backfiling and Amending CTR , Issued September 10, 2013. We need to notify our regulator. I explained this was not a backfiling, our regulator did not discover this error. The only error ws the state for the ID.
I have not notified the regulator in the past-thought this might be something new?

Amending a single CTR does not require that you notify anyone. You just file the amendment and move on.

That's what we did and moving on!