The Deputy Season 1 Episode 18 Silent Gun

A mute gunfighter with a distinctive scar around his throat arrives in Silver City and proceeds to provoke two gunfights, resulting in the deaths of the two citizens. Even though the mayor and town's business leaders demand action, Marshal Lamson can't arrest the gunslick because he didn't draw first either time. Clay attempts to find the reason for the gunman's apparently senseless vendetta.