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HPD responded to the Memorial Towers apartments near Memorial Drive and Detering Street to a shooting call after someone reported that a man had been beaten and shot.
Officers learned of an argument between a man and woman believed to be in their 40s or 50s.
According to police, they were arguing over one of them leaving their shared apartment.
The couple reportedly had an "on-and-off-again" relationship with a violent history that was never reported, police said.
The man was said to be assaulting the woman, which led the latter to shoot the man in his torso, police said.
According to police, the woman did exhibit physical injuries that indicated abuse. She was not placed under arrest or detained.
The man was taken to the hospital, where his condition is unknown.