Mr. Michel can add to my answer, but the system in Quebec is different from that in other provinces.
First of all, if police officers respond to a domestic violence call and have reasonable grounds to believe that a criminal offence has been committed, they will lay charges, even if the victim doesn't file a complaint. This ministerial policy was adopted by the Government of Quebec more than 20 years ago, so it has had some effect.
Furthermore, in Quebec, we file a complaint with the prosecutor, who then decides whether to lay charges. I know that in other provinces, such as Ontario, it is the police officer who lays charges directly, and the proceedings follow. Mr. Michel is probably in a better position than I am to answer you.
