There are several agencies I would look toward for personally owned weapons policy.
Your best bet is the Las Vegas Metropolitan Police Department. They don't require you to buy your own weapon but they strongly encourage you to do so by issuing a second generation S&W if you don't. I asked about this and they said that the "aren't in the gun business" and that as an officer, you should care enough to pick the gun the fits you best. They allow any 9mm, 40, or 45 from the major manufacturers, Beretta, Sig, Glock, H&K, even 1911's. I always cite them because they are a big agency that shows it can be done.
My agency, National Park Service, allows officers to carry personally owned pistols, shotgun, and rifles, provided that they meet our requirements - currently a Sig Classic in 9mm, 40, or 45. I currently carry my personally owned P220 in 45 and will soon be carrying my new P220ST as soon as the paperwork goes through.
I know that some other federal agencies allow personal weapons. The US Forest Service allows personally owned Glocks and Sigs and I believe that the Border Patrol still allows personally owned Sigs to be carried.