Louisiana

Section 1. R.S. 56:116.3(G)
A licensed hunter or tracker may pursue a deer that was legally shot and mortally wounded and dispatch the deer if the deer is found alive. Except in wildlife management areas, the licensed hunter or tracker pursuing the mortally wounded deer may utilize lights and a blood-trailing or tracking dog. No more than one dog may be used per tracking party in pursuit of the wounded deer, however a second dog may be utilized for the purpose of deer retrieval training. Tracking dogs shall be on a handheld leash or utilize a GPS tracking collar. Any mortally wounded deer, discovered alive after legal hunting hours, may be dispatched by the licensed hunter or tracker by using a centerfire handgun with a barrel no longer than six inches, caliber no larger than .45 or smaller than .25. The licensed hunter or tracker may pursue a mortally wounded deer onto private property only if he has received verbal or written permission from the landowner

State Regulations: https://www.wlf.louisiana.gov/news/governor-jeff-landry-signs-act-272-into-law-relative-to-tracking-mortally-wounded-deer-with-dogs

United States:
Canada:

Green — Tracking allowed
Red — No Tracking allowed
Gray — Tracking allowed under certain circumstances or in certain areas of the state/province, but not all