Who can investigate military accidents in India?
What exactly you mean when you say this?
Accidents involving Military Personnel and civilian: Police will investigate as it would in any other case of accident.
Accidents involving military person only: A military court of Inquiry will investigate presuming it happened in military area and both parties were doing their bonafide Military duties.
In case two military persons get involved in an accident while not on duty and/ or outside military area of jurisdiction then Police will investigate.
Accidents involving civilians when military is carrying out exercise in areas outside the designated Cantonment like, field firing, tactical exercises with troops etc. then it will be a joint investigation with Police in lead and military in supporting role.
If it is when military is called in aid of civil authorities like unrests, natural or man made disasters, then military will conduct its own inquiry and keep the civil administration informed.
You see military has special powers in areas where AFSPA (Armed Forces Special Powers Act) is in force then mostly the Civil administration is defunct and as it is unable to do its normal functions (that is why ASFPA is invoked) so all accidents involving them will be investigated by military itself.
It must be understood that military by far is the most neutral and fair in all its investigations and there is no reason to doubt its objectivity if it conducts its own investigations.
Design failures are investigated by the design and production agencies.
There was a case of the HAL Dhruv boom breakage which is being investigated by HAL.