Travel On Trains
From the official Amtrak site:
Only service animals permitted
We allow trained service animals accompanying passengers with disabilities in all customer areas in our stations, trains and Amtrak Thruway motorcoaches.
We permit no other animals onboard at any time.
Control of your animal
You must keep your service animal under control at all times and comply with local animal safety regulations. The animal should always be on a leash or in a carrier, except as required for boarding or detraining.
Please note that if at any time you lose control of your animal, or your animal causes a significant disturbance, the train crew may in its discretion remove the animal from the train and turn it over to local animal control officials.
Walking your animal
If the train schedule permits, you may walk your service animal at station stops provided that you stay within reasonable proximity to the train and re-board promptly when the conductor notifies you that the train is about to depart. If you plan to walk your animal during the trip, please notify the conductor when you first board the train.
Note: You may be asked what type of service your animal performs.