I've seen neighborhood barbecues where they send invites to the PD and the Chief or someone usually tells patrol "make sure you go by there and talk to some people since they sent us an invite".
You could also check and see if the PD has any ride-out programs or volunteer positions. Otherwise it would be a case of having to find out if any of your friends have friends who have friends who are local cops, kind of like the whole 7 degrees of Kevin Bacon thing, and then finding a way to get introduced.
Depending on what your profession is you could always drop off free samples or certificates at the PD too.
Last but not least, just wave one down and introduce yourself. "Hi, my name is John Doe and I live at XXX" then ask any kinds of questions you want, "what's your favorite (insert type of cuisine) place to eat?" or "I need to get my car worked on, where is a good, reliable, honest place to take it?" or any other number of things.
Be the guy who organizes one of those events you are familiar with from other towns.