The Davis Police Department and the UC Davis Police Department produce and distribute trading cards featuring police officers. To get your own, you can either be given one by a police officer, go down to the police station or trade away your first born son.
More information can be found in a Dateline article titled Cops' calling cards collect chums or in a Maxim Magazine article To Serve and Collect (link to archive.org, original page is gone).
According to an August 9, 2011, article in The Davis Enterprise, a 7th edition of Davis Police Department trading cards is newly available—the first set to come out since 2003. They include 41 officers and can be obtained, as in the past, by asking an officer or dropping by the police station.
From Dateline article. 
From Dateline article.
photo request: police trading cards
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omg I want DPD trading cards. Do they still make them? -KrisFricke
2005-02-09 22:53:03 They should give out their own card to everyone getting a ticket —ScottRitchie
2005-02-09 23:00:04 If only they made DCR trading cards. I'll trade you a KenBloom for a GeorgejAndrews. —BrentLaabs
2005-02-24 08:06:54 i am touched Brent by your trade proposal —GeorgejAndrews
2006-10-24 16:33:11 Neg, they do not Kris... I pester officers for cards as it was a well remembered thing from my youth, the most recent onces I have seen were 2005 series for dispatchers and people who work inside the station. Oh and scott, the backs of the cars have a blurb for the officers and then a place for contact info case number etc so they were designed with that in mind —StevenDaubert
2008-04-21 11:27:26 These are UCD trading cards, not City cards. My guess is that they are doing so bad in the PR dept that they only have really old cards and have had such a big turnover that it would cost too much to print because most (not all) of the good officers leave. The city isn't known for being too nice if they don't like you. —OurBuckle
2011-02-03 07:20:55 I'll be down with my unwanted offspring? Or maybe I'll just ask really nicely ha ha —JeremyBrandonBelk
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