It tends to look like a pouch for the PR24 Police Baton. More common in the US than the UK as many Constabularies here use the ASP extendable bit of kit which doesn't have the spar out of the side.

The way these pouches, if that is what is, works is that the baton goes in and then the snap / tie secures above the spar. It is then quite difficult to fall out but easy to pull if you need it.

Just an idea, might be wrong!!

Rich