In Australia, the various State Police Forces are responsible for any investigations into deaths that are not natural. As far as I know, none of the States routinely involves experts from the diving field when doing investigations into diving related deaths. There are a few exceptions, but that is more when the other people involved have insisted that the Police speak to experts (and not Police divers who are certainly not experts in recreational diving).
I spoke to the then just retired head of DAN Asia South Pacific a few years ago about trying to set up a system where the Police refer all diving deaths to DAN and some independent experts to provide advice. He told me that DAN already "investigates" diving deaths, but really, all they do is review publicly available information and make comments. The problem with this is that the publicly available information is, in almost all cases, not extensive or, for that matter, accurate.
As I have mentioned here before, I have been involved in the investigation of three diving related deaths. One of course was the Tina Watson death where the Queensland and Alabama Police had no expert involvement and if they had, it would have been straight away dismissed as a simple accident.
Another case was an American diver living in New Zealand who died in Vanuatu (she should never have been let dive on the wreck by the dive company). In this case, I got involved early and eventually the NZ Police (who were investigating the death for the Coroner of a NZ resident) contacted me and sought my views on a number of things, especially related to locations inside the wreck of the SS President Coolidge and comparing to the diver's dive computer and the dive guide's conflicting statements about what happened and where. In this case, nothing could really be achieved except I helped the incompetent dive company to close up and leave the country.
The last case was the death of a friend 10 years ago next week on a dive I organised and was on. In this case, I insisted that the Police officer who investigated (just a normal general duties officer, not a detective) talk to certain experts in dive medicine. This led to the Coroner making certain recommendations about further studies into IPE.
I know of at least two other deaths where the full details have been blocked from coming out publicly, presumably so that they would not sully the memory of the divers who died since they had stuffed up badly.
I have told my family and friends that if I ever die while diving, they are not to block any release of details about what happened, even if it shows that I fuc&ed up big time. It is only by releasing such information that other divers can learn from errors that proved fatal and that even highly qualified and experienced divers can and do make mistakes.