Coogan's Bluff (1968) on Netflix

Coogan's an Arizona deputy sheriff, who doesn't get along with his boss and doesn't exactly do things by the book, and also a little arrogant. Fed up with his rugged individualness, his boss sends him to New York to get a man who's waiting to extradited. Upon arriving everybody thinks he's just another bumpkin. When the New York Police Lieutenant tells him that his prisoner is still not ready to be transported, Coogan tries to be patient. But when he decides that he can't wait anymore, he tricks one of the attendants into releasing the prisoner and at the airport someone springs him. Coogan's boss is pleased that he has screwed up so bad, and orders him to return but Coogan feeling responsible or his ego has been bruised stays and tries to find despite being warn by the Lieutenant that he has no authority here.