I'm not sure about how "cop" is used, is it pejorative?
Anyway other Italian word to express the police officer are:
"agente di polizia", very formal;
"poliziotto" = most common, not very formal, but absolutely not pejorative: it's usally used writing news stories.
"gendarme" = antiquated, meaning something like "man of army";
"piedipiatti" = humorously used or pejorative;
"questurino"/"celerino" = popular, colloquial, sometimes used in newspapers.
"sbirro" = very pejorative.
Canadian native. "Cop" is informal and can be pejorative with intonation. I used "I will call the police" and it was not accepted because it is a "pluralized noun". I would not normally say "I will call A policeman". Here (rural Canada) they come in cars and are dispatched by a central call number. In the bigger centers there are officers on foot. I am pretty sure whichever form was used, intent would be established. ;) Other pejoratives are "pigs", "hogs", "smokies".