lost/unlost cats

Under a truck on the street where I'd parked was a glimpse of fur, which proved to be a very affectionate cat. Shaggy coat, though, which made me wonder if it was used to being outdoors. (I asked a jogger passing by, who was inconsistent.) I have a vague idea I've seen a "lost cat" poster somewhere in the area, but I couldn't find it along the route I regularly walk. In the mean time the cat hid itself somewhere. No matching "lost" ad in the Times.

What's the right procedure for a questionable cat? Any tips for guessing whether it's supposed to be out?

I wouldn't let a cat run outdoors in the city, but I'm suppose some people would on this side street. I'd certainly give it a tag. But maybe bundling what might be some unwise person's outdoor cat into my car and driving off is too much. Or maybe it wouldn't have been.