Before you begin to search for the helicopter on the map, first of all you should know that the handling and speed characteristics it differs from the military one. Not to mention cargo helicopters and helicopters for news.
You simply will not succeed to get the police helicopter in the beginning of the game. You’ll have to pass several missions before the most part the main map will be available for you. If you don’t want to pass GTA by yourself, just download safe with opened map.