I would say that vermouth kills all those she impersonates, and takagi would be dead.
About that department i think he wanted to give the correct deduction since he is detective in some way. All BO members must have a phone with them or some device which they keep in touch all the time. He used the other phone to leave no trace to him, and the handkerchief was simply to avoid finger prints.
@ karan
if you dont have something to say about this dont post stupid smiles, to achive more post AVG. - mod fixed by Chek