They renumbered the precincts in the 80s or early 90s, before I came on, but Conant and Davison would be the 11th Precinct. Now, it's in a newer building on Nevada by Mound. The last few years they've been combining and splitting the precincts over and over. The 11th Precinct is now known as the Northeastern District, it's a combination of the old 7th and 11th Precincts.
Your gun is from either the 5th Precinct (now known as the Eastern District, a combination of the old 5th and 9th Precincts), or the 12th Precinct, which is once again the 12th Precinct, as they're dividing the districts back into precincts.
Here's a map of the old precinct boundries:
And I THINK this is a photo of the Conant and Davidson building you're speaking of: