Again, it varies, but a lot of places have moved to a central dispatch model where basically everything, emergency and non-emergency, is going through the same dispatch center in one way or another.

In the area I work in, especially after hours and over the weekend, a lot of stations aren't staffed and everything redirects to us anyway, and even if you do reach someone at the station, often they're either going to transfer you to us at central dispatch, or take down the information and call us themselves after they hang up with you. They're not able or not supposed to dispatch much of anything from the station directly.

Technically those calls go behind 911 calls in our queue than calls on actual 911 lines, but luckily in my area our staffing and call volume are at a level where that's almost never a factor and pretty much all calls are answered immediately.

So most of us here are of the opinion that people are better off just calling 911 for anything except for basic administrative things that need to be handled by the office at the local station, basically everything else needs to go through us so you might as well cut out the middle-man and go to us directly. And worst-case scenario we can't help you and we'll tell you who to call instead (you really need to be a major nuisance before anyone even begins to think about trying to get you in trouble for misusing 911 for a non-emergency, none of us want the paperwork or to have to go to court or anything else that would have to go with that.

Again, the situation varies a lot from place-to-place, non-emergency lines may be more useful in other areas, call volumes and staffing levels may be worse and you may not want to tie up the 911 lines, etc. so it pays to be aware of the situation in your local area.

Again, this all varies, but that's pretty much how things seem to work everywhere within a couple hours of where I work.