? Not sure, it says an adjacent circle but it makes sense they could
Police move along the black squares on the game board, as opposed to the wretched and Jack, who move along the numbered circles. Policemen can only search for clues or arrest in a circle that is directly connected to their black square (crossing).
There may be some confusion since some crossings are offset where the dotted line extends from another dotted line instead of the crossing. This offset crossing does not impede Jack's movement along the dotted line. Here is a link to better explain: