All complaints should be made by the complainants and or their representatives. This procedure should follow normal rules for legal proceedings and should be instigated entirely on that basis with full security, confidentiality provided to protect victims and complainants at all times.
Who has ever heard of criminal suspects referring themselves for investigation and prosecution? It is an absurd notion.
So the police should not refer themselves for any criminal or other matters of public interest and concern, but be required to cooperate and provide evidence as from a public body for due investigation by non-political, non-police influenced members of a new authority vetted for competence and independence and appointed for fixed terms.