We don't know...
However, it's heavily implied that because he is actually innocent, he will escape punishment.
The implication in Barr's hospital room is that, with Helen's DA father in attendance, she coaxes out of him the way that Barr would have done it which, of course, does not match the known facts....thus proving to her father that Barr is innocent.
Also, he is afraid of Jack, although he asked for him in the first place.
His fear is that because he's done this in the past and everyone else thinks he did it this time that Reacher will come and exact justice on him.
Of course, we know that Reacher has already been to the city, realised that Barr is innocent, and taken steps to solve the case.
Here's a synopsis from IMDB which covers the same territory
Helen is concerned about clearing both he and Barr from any murder charges. Jack tells her he thinks that she and her father will be able to work that out. Jack and Cash jump in Cash's truck and take off as the police are arriving. Helen is upset that Jack is leaving, that he will disappear again and she won't be able to find him.
Helen goes to see Jack Barr, who's out of his coma. He doesn't remember the shootings, but heard the nurses and cops talking about it. He figures if they said he did it, then he did it, because he'd done something similar before and got away with it. With Alex Rodin standing nearby listening, Helen shows Barr photos of the stadium, parking garage and bridge and asks him how he would have done the job. His assessment is exactly what Reacher said it would be.
Helen tells Barr he's going to be all right, that she's going to take care of him, but he is remembering Jack Reacher's promise to come get him. He figures he's a dead man. Helen will no doubt explain that to him later.