I did a circling approach from an ASR at KCMI a few weeks ago, and the controller asked us to tell him when we wanted to circle. Then I asked him how close he would let us get, and he seemed to be ****ed off that I asked instead of told him I wanted to break it off at a half mile or something. I was with a student and didn't want to break it off too soon, so I was trying to be nice and find out what would work for them. From what I remember, he cleared us to land and told us to contact tower upon landing like they normally do. This was in VFR conditions on an IFR flight plan, but the winds were gusting to like 27kts and almost a direct crosswind.

Aside from the confusion of him asking us when we wanted to circle and me asking him what would work best for tower, and him getting ****y about it, the rest of the approach and landing/taxi was pretty straightforward. I'm sure different facilities do things a little bit different.

I usually take my students into KSPI because they are usually happy to give us whatever we want. Their approach controllers will usually clear you to land, and give you your on IFR clearance to leave the airport (if on IFR flight plans) and give on the go instructions, and you do the approach, tough and go, and never contact tower. Although one time because of a crosswind we did a go around and asked to land on a different runway and they told us to contact tower. I can't specifically remember if I've done any other circle to lands off of ASRs.