Here in DC, DDOT places a laminated card onto bikes that have been noted as abandoned. It has a date on the card, and gives the owner 30 days from said date to remove the bike. After that, DDOT can remove the bike with whatever method works, up to and including destroying the frame.
But the cards are very easy to spot and clearly worded - and effective, from what I've seen. Perhaps NYPD could be so clear.
Oh, wait a minute - it's the NYPD. Nevermind.