What Happens in Atlantic City - S2-E2
Trivia: O'Donnell references "James Barr" as someone who might have a grudge against the 110th. Reacher says he "ran into him in Indiana last year - he owes me now." That's a reference to the book "One Shot", which was also the basis of the Jack Reacher film starring Tom Cruise, where James Barr was falsely accused of sniping civilians. That story's presumably canonical in this series but is now in the past.
Answer: As Reacher had arrived in town just after the murder occurred and being a stranger, he became a suspect (or at least a person of interest) and taken into custody for questioning by the police. He was released fairly quickly. It was coincidental timing of an outsider arriving at the same time as the crime occurred.
raywest ★