Re: another one for the military buffs
Depends on how militarised your society is – from the brief you state this is an army problem, so no civilian agencies either exist or are involved?
The closest example of a quasi-civilian establishment I can offer would be the old USSR Militia – a paramilitary police force but with state prosecutors (investigators and detectives) in a parallel branch of service. If you want hard-core then go with the tried and trusted KGB model.
If your fugitive is being hunted by military intelligence then, again, it depends on whether there is any degree of civilian oversight and/or involvement. Purely military organisations tend to co-opt less formal (and thus deniable) resources for ‘squishy’ problems (i.e. one that isn’t simply point-and-shoot).