Police have charged 36-year-old Richard Lee Johnson with murder. The victim has been identified as 33-year-old Antonio Dixon.
Police say the victim and the suspect knew each other and the incident was not a random act.
Police said the shooting did not involve the health center, which was briefly locked down during the incident.
People, however, were still rattled because the shooting in an outside stairwell was so loud they thought they were in the line of fire.
"It was horrifying," said eyewitness Amanda Seitter. "People [were] running out the door just trying to get out. I mean I don't think anybody knew really what was going on."
Two men seen running from the scene are no longer being sought because police say they did not take part in the murder.