PSP are by law in the Game Code allowed to enforce the game Code and they may and do put down injured deer. This is who the law allows to enforce the Game code:
§ 131.3. Enforcement.

In addition to Wildlife Conservation Officers or Deputy Wildlife Conservation Officers, the Director designates and empowers the following persons to enforce the act and this part while acting within the scope of their employment and jurisdiction.

(1) Pennsylvania State Police.

(2) Pennsylvania Waterways Conservation Officers.

(3) Pennsylvania Deputy Waterways Conservation Officers.

(4) Pennsylvania Department of Conservation and Natural Resources personnel with enforcement powers.

In addition to the above the Commission may approve municipal police to enforce the game Code as well as federal agencies with law enforcement power. However, unless things have changed since I retired they have not authorized any police departments to do enforcement and Federal agents for US F&W assigned to PA are made Deputy WCOs.