Stranger on the Run (1967) on Netflix

Plot summary

Ben Chamberlain arrives in a railhead town asking about a woman. He is a former inmate and a heavy drinker, and the town is run by Sheriff McKay, whose deputies are quick to use their guns. The people Ben questions will not talk about the woman, and he takes a beating just for asking. When he leaves town, McKay takes him for the killer and sets the blame on him. The sheriff gives him a horse and some supplies and an hour's head start toward the desert, and then the posse rides out after him. Ben's only way clear is the border.