Does a villager only ask you to add a police station (or other public works) when they approach you?

I know that the Police Station is a public works project that must be requested by one of your villagers.

I also know that villagers will see you, an exclamation point will appear above their head, and they will walk straight to you until you talk to them or ignore them.

My question is, will they request a public works project only in this case? When they approach you? Or can they request it during any conversation, even if they don't approach you first?

Solution 1:

Villagers will only request public works projects when they voluntarily approach / "notice" you. When you initiate conversation, they may try to ask you for different kinds of favors, but never suggest public works projects.

This, of course, includes the police station. The exclamation point above their head and the tell-tale sound indicate them noticing you.