Mr Dunne's phone and and meta-data records were accessed without his permission during the David Henry inquiry into who leaked a report on the GCSB to a Fairfax journalist.
The full email trail between Mr Dunne and journalist Andrea Vance was mistakenly sent to the inquiry by Parliamentary Service.
It sat on the parliamentary server for 5½ hours before it was deleted.
Mr Dunne has asked the Speaker to look into whether the file was read in that time, and by whom.
He said the Speaker had told him detailed work will be undertaken to find that out.