It’s the same for police. The exception are when there is a fiduciary relationship, if you created the peril, or if you start rescuing someone you can’t leave them worse off. Usually these exceptions don’t apply to police, even if you call and ask for help, they have no duty to act.
Clear takeaway: when they said “Because this complaint was made directly to the police department, we are obligated and have a duty to examine the complaint further" it really means they wanted to do it but didn’t want to be held responsible for wanting that. (after all, if they had no choice in the matter it’s not their fault they’re doing ghoulish police-state things most people don’t want done)