Little Rock police have identified the victim of Saturday night's homicide as Evilio Castro-Alverez, 55.
It is the fifth killing reported in Arkansas' capital city since Monday.
At a news conference Sunday, Lt. Steve McClanahan said officers were called to Spanish Valley Apartments at 5300 Baseline Road around 10:33 p.m.
They found Castro-Alverez lying outside one of the apartment buildings, McClanahan said.
Police are now searching for a man who was seen running through the area with a gun. McClanahan said they believe the man was trying to rob Castro-Alverez.
No arrests have been made in the slaying, which is the 37th homicide in Little Rock this year.
Four other killings have been reported in the city since Monday, including two in the last two days.
On Saturday night, police identified the man found fatally shot inside a Jeep Cherokee that crashed into the Berkley Apartments at 1601 N. Shackleford Road about 11 p.m. Friday. Carlo Marigliano, 31, is from Italy, authorities said.
Steven McPherson, 43, of North Little Rock was shot at the Big Country Chateau apartment complex at 6200 Colonel Glenn Road on Thursday night and later died at a local hospital.
Shootings reported within minutes of each other at separate locations in the city Monday night left a 14-year-old boy and Loren Robinson, 30, dead.
No arrests have been made in any of those killings.
Read Monday's Arkansas Democrat-Gazette for full details.
Hunter Field of the Arkansas Democrat-Gazette contributed to this story.