Yep, as soon as an animal leaves one state it becomes the management responsibility of the neighboring state. I believe all wildlife is owned collectively by their respective states and then a seperate state agency such as a "Fish and Game" agency is charged with protecting and managing as the state sees fit.
Here is a response I copied from "John S" a retired WCO of the PA Game Commision on this very topic:

As per Section 103 of the game code of PA:

"They are owned by the state, held in trust for all people of the Commonwealth and the PGC has been charged by law to manage and protect them for the common good. "