A local or county historical society would love to have them. If there isn’t one close, contact the Indiana state archives at https://www.in.gov/iara/

Just to add to this and if all the other suggestions are not available, the Indiana Historical Society would probably be quite interested in this material. They can hold material of interest from Hoosier communities that do not have local archives and that cannot be held in the Indiana State Archives - Here's their collections policy https://indianahistory.org/wp-content/uploads/copy_of_collectionspolicy.pdf

You should contact the sheriff office he worked for. A lot of them have their own museums within the office.

If you have a local history museum in the town he worked they very well might be interested. The local history museum I worked at as an undergrad had plenty of things like this. They can be helpful for people who might be doing research into the town's police force or into just policing in general.

Source Worked in two local history museums both of which would have happily accepted these even if they would not necessarily be able to use them as a display item.

Hey OP, I'm actually a graduate student in the museum studies program at IUPUI and have worked in a number of the collecting institutions here in Indiana and I'm currently working in one of the local archives. I'm going to go off of a number of the answers that are already here and help give a little more background to them.

Your local county museum likely would still be interested. While their "scope" of actual displayed objects and interpretation of history is mining, their mandate is likely all county history. Our program is working with the Wayne County Historical Society, which, while they are focused on displaying the collection of this one person who founded the museum, they are really mandated to look at the rest of Wayne County history. Your local museum will be the same.

I would avoid any organization you don't see as solid. If you as an outsider don't see them as a potential repository, it likely means that they don't have the means or ability to care for the collection, let alone storage space.

The State Archives, as well, would likely not be a good option. The State Archives is a place that handles governmental documents. While your hand-written notes were done by a government employee, your sheriff granddad, it isn't an official document. They already have their hands full with the official stuff; they aren't going to necessarily be able to give proper attention to this collection.

The Indiana Historical Society would likely be incredibly interested. They live for this sort of thing, and have done a push lately to do a lot of "microhistory." They also have the capacity to handle your collection and to properly treat it, and it's within their scope. They're also a wonderful bunch and would likely be very easy to work with (not saying anyone else here isn't wonderful. Just from my interactions with their staff, they're particularly wonderful).

You could also consider the Indiana State Museum. They are sorta quasi-governmental, and while they have their fingers in a lot of baskets, this sort of thing would likely also be pretty interesting to them. Again, they have a more museum and material culture focus, but if the other options fall through, they would likely have the capacity to handle the collection and ability to care for it, and it would be in their scope of collecting.

Finally, IU might be able to handle the collection. They have a bunch of collections that span many, many areas. One of my professors this semester is their director of collections, and if you can't find anyone else to take it I can get you in contact with her.

Just to re-iterate, here's my list of organizations that I would look to.

1. County History Museum

2. Indiana Historical Society

3. Indiana State Museum

4. Indiana University

Chances are, out of these four locations, one of them will take it. Hopefully this helps OP, feel free to PM me with any questions.