Update, 9:55 a.m.: The suspect in the fatal shooting has been identified as 42-year-old Christopher Clark.
He was arrested coming out of the woods behind the Planet Fitness at 1600 Fort Campbell Boulevard shortly after the shooting, and was taken into custody without incident, Beaubien said.

Clark has been charged with criminal homicide, according to the Montgomery County Sheriff’s Office booking log.
Police have also identified the victim as 55-year-old William Eakes Jr. His next of kin has been notified, and at this time, there is no known connection between Clark and Eakes, Beaubien said.
Previously:
CLARKSVILLE, TN (CLARKSVILLE NOW) – A man was shot to death in front of the Walmart on Fort Campbell Boulevard late Tuesday night.
At about 11:54 p.m., Clarksville Police responded to a shooting-in-progress call at Walmart, 1680 Ft. Campbell Blvd., according to police spokesman Scott Beaubien.
Police found a man with multiple gunshot wounds near the front doors. The man was taken to Tennova Healthcare-Clarksville and later pronounced dead.
A suspect has been arrested, and the Clarksville Police Department does not believe there are any other suspects at large and there is no threat to the community.
No further information has been released.
Witnesses reported there was a lot of blood at the scene, which was being cleaned at 7:30 this morning.
Detectives with the Special Operations Unit and the Crime Scene Unit are investigating.
Anyone with information or additional video footage is asked to please contact Detective Goble, 931-648-0656. To remain anonymous and be eligible for a cash reward, call the Clarksville Montgomery County Crime Stoppers Tipsline 931-645-8477, or go online and submit a tip at P3tips.com/591.
Correction: The shooting occurred Tuesday, March 1. This article has been updated.
Keely Quinlan contributed to this reporting.