Agile and scrum in managing (criminal) investigations

What outcomes are you hoping to achieve from agile practice? How would they differ from the outcomes being obtained now?

I can only give an opinion as I am not familiar with investigative work.

In general, I believe Scrum can be beneficial, if as a starting point one can construct a prioritized backlog with work (cases) or product items, and a self-managing team can pull items from this backlog. The two critical starting points, in my opinion, are a prioritized product backlog and a self-managing team. Once the above is in place, the Scrum framework—with its events and artifacts—can be implemented, allowing the process to evolve over time.

For Scrum to give value the items in the product backlog need to be prioritized, and the self-managing team takes responsibility for the backlog items they pull to work on as a team. 

Thank you so much for your replies Ian and Pierre. 

Ian- Outcomes: Increased overall throughput by spending less time on cases we end up closing (while still conducting a due diligence investigation). I see this as our biggest constraint. 

Pierre- I like what you said and how you said it. Yes! A prioritized backlog the self managing teams pull from. We have case reviews (sprint planning) every 4 weeks (sprint) with each agent concerning their caseloads (~18 cases). An investigator obviously can't work them all in a 4 week sprint. We prioritize the cases they need to work on on what needs to be done for each case. I am thinking I need or can design a simple tool to make those sprint backlog items more transparent. 

From what you describe there are no significant risks or uncertainties to mitigate on a Sprint by Sprint basis. Can you give examples of the kind of Sprint Goals that need to be addressed so innovation is then harnessed?

Paul, I have not so much knowledge about how this type of work usually runs. 

I can only relate my opinion based on my time when I was working for gov sponsored/subsidised company.

Some types of work being done were bound by rules & regulations according to a defined set of governance policies. There was some wiggle-space for odd cases, though usually if an odd-case proved to be a pattern then it was also codified into processes according to rules & regulations, so on. 

I don't know how criminal investigation works in where you live, no idea about how legal things run there.

I can only guess that you have some governance that you need to follow and procedurally work cases up in a linear manner and close them with some sort of formal closure - if there's enough proof/evidence (don't know which term means what in your context) then a case can be solved with a legal trial or whatnots. I also guess that there are some cases where there's not enough proof/evidence so the case needs to be frozen or closed, but can be reopened when new proof/evidence arrives on the scene.

I also guess that there are some pain in the ass cases where the damage to legal system and society is minuscule, but it's still like a mosquitoes flying around - idk, spray painting grafittis on statues, monuments, inside metro stations, whatnots. 

Maybe also traffic & parking tickets.

Dunno. 

That's my opinion, as I have no more info on your context I can only end here.