I was able to go to the police station and request a neighborhood report that listed incidents over a one year period at or near the property.

You've likely already got liability insurance on them at the same dollar amount as your limit of insurance for replacing the building but the umbrella adds a nice million or whatever per incident to make sure you have enough "lawyer go away" coverage.

One of the incident for which one of the homeowner had fake lawn installed on the front (that's being prohibited at the time) but was able to get every one to vote in order to overturn that restriction.

Let's say there's a slow water leak under the kitchen sink or another incident where the tenant may want to put off calling.

There are just times damage is done to the property and a quicker call helps respond to what ever the incident.

Overall, it’s a very quiet neighborhood, with this rare incident.

Further, If there was a fire or incident as a result of major construction, you wouldn't be covered if you didn't have a construction/ builder policy in place beforehand, which calls for having insurance before work start.

If so: yes, I had more coverage per incident.  

I would also ask the tenant to explain the circumtances surrounding the shooting/robbery to see if there was anything they were doing, or about the property itself, that attracted any undue attention from the suspect or that could be changed to prevent another similar incident for happening. 

I know in the cab business there are guys that get beat up all the time then there are those that go 35 years w/o incident.