If you lost something in a green taxi, the City will help you get contact information for the taxi's garage.
You should then call the garage directly to see if they have your item and arrange to pick it up. You should also call the Police Lost and Found Center in each borough to see if your item was turned in there.
You are more likely to find something you left in a green taxi if you have the taxi's license number. This is the five letter/number combination for the taxi located on the taxi receipt, on the side of the taxi, and on the partition in the taxi.