I had a look through the historic newspapers, and I couldn't find anything about a John Smith, policeman, dying in the line of duty in the 1860s.
I did find another story about a John Smith policeman, getting into trouble for theft, but that man was 28 in 1867, so likely too young to be your John Smith. And as you say, such a common name, it would be hard to be certain it was him anyway. Also, he seemed to be living in police quarters, which I don't think a married man would be doing.