What is the law on properly displaying your registration in New York City?

My car was towed in New York they other day. They wrote me a ticket at 7:12 and then towed it at 7:14. Is it legal for them to tow your car that soon after the ticket is written? Also, they wrote me a ticket for improperly displaying my registration on the vehicle. It was on the dashboard, because the adhesive wore off. What does the law say about posting a registration on your vehicle. The vin, expiration date and bar code were all visable.