Batesville Police identified the man killed as 37-year-old L.C. Webb Jr.
Family members confirmed the woman shot is Tabitha Sanford Webb, and said that her husband shot her. They say she is in critical condition.
A friend of the family said it happened in front of their young son.
According to the Batesville Police Department, officers discovered two vehicles in front of the police department around 1:30 a.m. Tuesday. One person was already dead while a second was flown to the Regional Medical Center in Memphis for treatment.
Authorities with the Panola County Sheriff's Department said the shooting was the result of a domestic incident. They are not seeking any other suspects.
A woman who was driving home from work and saw the crime scene outside the police department after the shooting described what she saw:
"I just saw a dark truck at the police station, and a van. Both doors and the driver's side were open, and the police were there. An ambulance was there ... and I saw a child standing there with a police officer. I said, 'Well it’s domestic violence,' so I just went on home," she said.
"I guess it just happened because the police passed me. ... Later on, coworker said it was a killing at the police station and I got scared then because, man, I didn’t know all that was going on."