What reference from current insitution is required/advisable for pre-tenure move?
I don't think any contact with your current department is expected. Generally you are only expected to provide references who will write letters on your behalf, and it's not required that any of them be from your current department. Academic circles are small, and somebody in your department may find out anyway. Hopefully their reaction will be to incentivize you to stay.

When I have been on hiring committees, we never sought a contact within the current department. If you are shortlisted, then the committee thinks you're pretty amazing, so why would they suspect you are being forced out? My experience is with heavily research-focused departments; this might be different, say, at a small liberal arts school.