Pets must remain in a soft or hard-case pet carrier, which counts as a carry-on bag, and you must book a coach seat (not first class, business class, roomette or bedroom).
Are pets allowed in Amtrak Starlight?
However, pets are allowed on the long-distance Coast Starlight and California Zephyr, which also travel in the state. To see more about pet travel on Amtrak, go to the Pets on Trains page on the railway's website.