Sibley Bike Depot in St. Paul, MN periodically gets donations of police department bikes.  They are usually given to us by small suburban communities (St. Paul and Minneapolis auction their bikes off to raise money).  Our police dept bikes come with no programmatic strings attached - we can do whatever we want with the bikes.
 
For small or start-up coops, police departments can be reliable sources of bikes.  Often they want you to be either a 501c3 or have a sponsoring organization but not always.  Especially for small townships, it isn't worth their energy to auction the bikes off - it just doesn't make enough money to be worth it (distinctly different than a place like Toronto or Minneapolis or other medium to big cities).
 
I would warn folks that police department "donations" can be useful but can also be a huge pain in the butt.  2 month ago, we got a load of like 75 bikes of which they were pretty much all worthless and we had to remove the rubber and such to recycle all of them - basically it was a bunch of extra work for us to process abandoned junk.
 
In terms of bike acquisition - I think that doing "bike drives" of various sorts - with churches, businesses, neighborhoods, etc can be a more effective way of acquiring decent bikes for all your different bike coop programs.  It also gets the word out to lots of individuals who potentially become supporters of your organization in different ways.
 
Jason Tanzman
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Sibley Bike Depot
Volunteer Coordinator
612-232-2737 (cell)
651-222-2080 (shop)
www.sibleybikedepot.org
Sibley Bike Depot's mission is to be an open, accessible space to educate and empower people to use bicycles as transportation, helping to build a sustainable environment and community.  Volunteer with us to help build a bicycling movement in the Twin Cities!