Traffice ticket 1 hour after offense? New York

I rear ended a car. The officer arrived on the scene 1 hour after the accident. The damage was minor, and has already been settled. The officer then gave me a ticket for following too closely. When i tried to defend myself he told me that he will give me a ticket for following too closely or for having an unsafe speed on a ramp, my choice. Do i have a case?

I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney client relationship.

Yes you do**************he doesn't know what happened and he didn't witness it.