I thought my way made more sense because the monk had met the guy and the cop hadn't. Would have made more sense in the OP also IMHO.

So it turns out the poor fellow had a twin brother. The brother heard about his twins misfortune and decided to go ask if he could ring the bell in his brother's honor. The monks said yes and he was led up to the bell tower just before noon. 12 came and he gave the rope a mighty pull, the bell rang once, swung back and knocked him over the edge. The horrified monk ran downstairs to find the same constable covering up the body. The constable says " I don't know who this guy is, but he's a dead ringer for the guy whose face rang a bell."

I laughed so hard at this I almost fell off MY perch!