I would suggest: "The police wear black hats" or "Police officers wear black hats" if this is a general statement about the police service. If it's about an individual officer, "The police officer wears a black hat." (With some local exceptions, "police" usually refers to a police service, not to an individual police officer. At least in North America!)
The policeman or police officer wears a black hat. Policemen or police officers wear black hats. We could say "the police are looking for him," but we tend to say that when we are talking about them as an institution, not with something so individual as wearing a hat. I think we might hear it if talking about the form of the uniform, e.g. "Jakarta police wear shorts," (I have no idea what Jakarta police wear) but it's a pretty rare usage.
Should be either 'The policeman wears a black hat' or 'Police wear black hats'.