Because, as I said above, I'm no longer interested in this bike (no room for another), and because this area is a bit of a special case. I could go to five different police precincts, ask what the story is with abandoned bikes, and get five different answers. Mostly, this is the kind of thing the police really aren't going to care about one way or another, and they're certainly not going to be enthusiastic about finding out exactly what the rules are and what the police department's policy is in this situation. If there is a policy. At this point, this discussion is entirely abstract. I was surprised this thread was even still alive.

What seems to happen here in NYC is that if a bike is left in one spot for a long time, and it's in an obtrusive place, the owner of the property on which it's locked up will remove it. If it's on city property, every now and then the city will remove it, but that doesn't seem to happen often. If it's in an out of the way spot, it could stay there for months or years. I've actually seen this happen. If it's a half-way decent bike, eventually it will be stripped of any usable parts, leaving nothing but the frame and perhaps a rusty chain.

Suggestions about contacting the local sheriff, or seeing if the bike is registered, or leaving a note on the bike, are well-meaning, but don't have any bearing on the way things work in New York. There is no sheriff (OK, there is a sheriff's department in NYC, but it isn't what you might think -- the sheriff's department collects on judgments). Your typical beat cop doesn't want to be bothered with stuff like this. A note left on the bike would be gone in short order. Or overlooked among all the other garbage that's accumulating on this bike (coffee cups and empty bags, newspapers, etc., stuff in the spokes, between the fork and the wheel, all over the bike).

As to qualms, this bike has been exactly where it is since April. Maybe longer. I can't remember when exactly I first noticed it, but it may well have been in April, or even March, and it had obviously been there for some time even then. It's abandoned. No question about it.

But it's a moot question now. Thanks, everyone, for the suggestions, some of which were actually kind of helpful, or will be, if I ever run across this situation again at a time when I'm looking for another bike. As to the accusations or near-accusations of thievery or lack of a moral compass, well, this is the internet, and everyone's got an opinion, and nobody has to back up their opinions. I'm no thief. I've never stolen anything in my life.