Misti Romero, 40, of Youngsville has been identified as the victim, according to SMPSO.
SMPSO said that around 2:45 a.m. on Nov. 24, deputies responded to the 1100 block of Evangeline Thruway in Broussard and located Romero dead in a business parking lot.
During the investigation, Andrew DeRouen, 54, of New Iberia was identified as the suspect.
According to SMPSO, DeRouen was found dead at a New Iberia residence from a self-inflicted gunshot wound.
The investigation remains ongoing. No further information is available at this time.