The Commercial Appeal reports officers picked up 32-year-old Jelani Greene after receiving a call Saturday about a naked man walking down the street.
Police Chief Don Gammage said Greene was taken to a house where 33-year-old China Lashella Jones also lived.
Gammage said Jones was found dead. Authorities have not detailed the investigation nor said how they believe Jones died, but they have classified the incident as a homicide, the first of the year in Olive Branch.
It was not immediately known whether Greene had an attorney.