 When Marcus shows his badge to the exterminators in order to  commandeer some of their equipment so they can get into Tapias  mothers house, if you freeze the picture you can read Marcus badge  clearly. He is a Lieutenant with the Miami PD. In the original  _Bad Boys (1995)_ (qv), when Marcus holds his badge up to the  peephole for Julie to look at, you can see it says "Sergeant", so  clearly, in the intervening eight years, Marcus was promoted.