So, I was going to mention this to you before Stratos when we were talking but then we started discussing my problem villagers instead.
To get public works requests, it will happen when a villager sees you and has that ping sound go off with a couple lines appearing above their head. It's when they want to see you and talk to you. This could happen when you first start up your game and pass by the villagers who are out walking at that time. Only one of them will do it though. So, if you had 5 villagers walking around and 1 pinged like that, then the others will not ping. So, the goal is to get more pings.
Now a ping isn't always about a public work request. It can be many other things like villagers mentioning they will move, asking for new catchphrases, making a nickname for you, selling you items or even just having a conversation. However, since public work requests can only pop up this way, getting more ping requests means you'll have a better chance of a public work request happening. To get more pings, this is what you do.
Go into the water all the way to the water's edge and then stop and wait there. Note the time and after 6 minutes or more have passed, then swim back to shore and go looking for villagers. The first one you see will usually have a ping occur to them. Talk to them and see what they say. If you've gotten no public work request, then go back into the water and repeat. If you had a villager ping you but it wasn't for a public work project, don't worry about avoiding them for another ping. They could still request a public work if they ping again later.
You can only get one public work request a day so if you don't get what you want or want more, then you need to move on to a new day. If you look up more info on public work projects, you'll see that some are only requested by a certain villager. I'm at a point where I've gotten all the public work requests a type of villager can make with some of their personalities. In that case, I do try to avoid them when hunting for a villager to give me a ping. Since I'm pretty sure any villager can request a police station, I don't think you have to worry about seeking a certain type of villager but if you check and see that you've got a personality type from which you've gotten all or most of the public work requests you can from them, then that might be the best one to target for a ping since if they do request a public work, they will have a much lower public work pool to request from. How is that sentence for making you go cross-eyed?
If all of this still sounds quite foreign to you, here's a YouTube video describing and showing it for you. It also has some other tips like leaving your pockets empty or filled with things villagers don't buy from you.
Finally, a couple other things that may help you. I've noticed that if I'm really good friends with a villager, they seemed to request public work projects more than villagers I'm not so buddy-buddy with. So, keep friendship levels high. As well, you may experience a moment when you walk by all the villagers and none of them ping you. In that case, talk to one as it may be that they need to tell you a message first like "take a break, you've been playing a lot" because an hour has passed by. Getting that message cleared up allows them to ping again.
I've been doing this when engaged in other things like watching TV or cleaning up. I can just have my guy wait in the water for a bit, do a quick walk through and if no request is made, hop back in the water and go do other stuff until my next check-up. That's why I didn't see your first message last night and that's what I was doing in game. Hope that helps if you still want to do stuff in New Leaf. Also, clean up your town. It was so sad walking through it the other day and the amount of weeds that were there.