Do airports have their own incident/accident investigation departments? or they are restricted to the NCAA/Safety department only?
In the U.S. an airport will have safety teams and internal incident/accident reporting. This is more for airport operations and OSHA standards. It has little to nothing to do with what we typically think of FAA/NTSB incident and accident reporting and investigation. The airport’s team is strictly internal. Although, it may have to report to some external entity if safety laws and regulations were broken. Or, they may have some reporting obligations if Human Resource or labor laws were broken. All of this has more to do with the airport having to operate like any other large business or government entity.
The NTSB/FAA can, however, request at their discretion that an airport or its authorities participate in the federal incident/accident investigation.
More often than not, the accident investigation boards in Europe are a governmental unit independent of NCAA. The Board should be able to criticize and put requirements on all units involved in an accident/incident. This obviously include the CAA.
Departements and organizations are free to do an accident investigation. Availability to an accident site may be limited, though. E.g. IFALPA have a structure of their own Accredited Accident Investigator, available for any relevant investigations.