How to get people more cooperative with police questioning

In the In Death books, a lot of the people who are hesitant to talk to police have done something that's a little bit bad. However, Lt. Dallas is trying to catch a murderer, and it's more important to catch a murderer than to prosecute every little misdemeanour. So she quite often finds herself trying to convince someone that she doesn't care if they've done a little drugs or cheated on their spouse or had sex in an elevator, she just needs to know what they saw so she can stop the murderer.

When I read that Toronto police are canvassing 6,000 homes to try to find clues in Mariam Makhniashvili's disappearance, it occurred to me that - if real life does in fact work like the In Death books in this respect (it's possible it doesn't, because In Death obviously needs the cops to look sympathetic) - they might have an easier time of it if they publicize the fact that they aren't out to get you on minor things that don't really hurt anyone. For example, if they don't care if there's a bong on your coffee table, they should say so. If someone's testimony starts with "Well, I was just buying some cocaine from my dealer and I saw..." then they shouldn't prosecute for the cocaine, and when they go to see if the dealer saw anything they shouldn't prosecute for the dealing.

Perhaps they could also consider not running warrants on people they question unless it's relevant to the investigation. It would really suck if someone is open and cooperative, provides useful information and/or is readily eliminated, and then they run warrants on them and they end up getting arrested for some old shoplifting charge or something. I'm sure the police would get far better cooperation if it were public knowledge that we could trust them not to be hardasses about things that are irrelevant to their investigation.