Who governs it? if you are talking commercial mining it is landowners and Nebraska Department of Natural Resources..
There is some exploration in the area we prospect for the "rare earth minerals" the depth they are talking is below the limestone cap, at 300-1200'
http://www.quantumrareearth.com/ At Depth resources are "owned" by the state and permits are required for removal. I don't know the details of that.
In terms of recreation including recreational prospecting, the authority is the land owner adjoining the river..
The Natural Resource District, generally the NRD, and NDEQ are concerned with water usage and quality, sand and gravel operators have EPA discharge issues to deal with in terms of proper settling of effluent prior to discharge.
We are surface scratching in the river, and access to Nebraska Rivers is generally considered public with landowner permission. We barely moving a 1/4 yard of material in a day's effort.
We have no desire to setup a commercial venture.