The police may move 0, 1 or 2 spaces.
Rules, page 10
After consulting together, the detectives move their Policeman pawns. Each player moves the pawn(s) whose Policemen he controls, starting with the Head of the Investigation and proceeding clockwise around the table. The Policeman pawns are moved along the dotted lines. When moving, a policeman can move up to a distance of two crossings. Policeman pawns ignore numbered circles when moving.