From what I know, there is no oversight body for HPD.  The commission is not part of HPD, so, they do not have any influence of an rules and or regulations nor any general orders that govern HPD.  All they do is hear complaints and now they are tasked with the hiring and firing of the Chief.

If there are any issues with the Chief, the commission not hear of it unless someone makes an official complaint...which the chief can, sometimes, squash.  Oftentimes Times. More so than not, the commission cannot subpoena any police reports to help them with resolving a complains.  And, many times, the reports and or documents that they get are redacted...I think it is because the commission is civilian board and not prived to police report until they are deemed public information.

Anyway, the past commission...going back to Dan Lin and Keala...maybe even Gibbs era, commissioners carried badges and could carry a firearm.  Did this mean they were part of HPD and prived to all reports?  Maybe.