But now they say even though four suspects have been charged in connection with the case, just one of them is accused of pulling the trigger.
Marvin Banks, 29, appeared in court on Monday and was charged with two counts of capital murder, along with counts of grand theft auto and being a felon in possession of a firearm, Mississippi Bureau of Investigation spokesman Warren Strain said.
Preliminary autopsy findings revealed that one officer was shot in the back, and the other was shot in the face, Strain said.
Investigators haven't said what motive they believe Banks had for allegedly opening fire, or specified what role the other suspects played in the shooting. Tests have begun on boxes of evidence, but it could be weeks before the results come in, Strain said.
"There are theories, but we'll wait on the forensics to come back," Strain told reporters.
Marvin Banks' half-brother, 26-year-old Curtis Banks, was charged with accessory after the fact of capital murder, Strain said.
Joanie Calloway, 22, was originally charged with two counts of capital murder, but her charges were reduced in court on Monday to accessory after the fact of capital murder, Strain said.
Cornelius Clark is charged with obstruction of justice.
None of the suspects entered pleas in court Monday. As deputies escorted him into a police station Sunday, Curtis Banks wailed and repeated "I didn't do it."
Slain officer had 'fire in his soul' for police work
Tate, they said at a vigil honoring the slain officers, was a rookie cop known for his big smile and the joy he got from blaring his cruiser's siren as he fulfilled a lifelong dream of being on the force.
Deen was a self-described "country boy" who loved busting gangs and became the department's police officer of the year after rescuing a family from a burning home.
A funeral for Deen, a K-9 officer who was married with two children, is scheduled for Thursday.
At Monday's vigil, his colleagues described him as an officer who made many drug arrests with his dog, Tomi, at his side.
"He loved to fight gangs," Assistant Chief Frank Misenhelter said. "He loved to identify them and figure out their strategies. He did that feverishly, passionately."
Tate graduated last June from the police academy, trumpeting the news on Facebook. At Monday's vigil, Tate's fellow officers said his joy on the job was infectious.
He'd worked at auto parts stores for years and was thrilled to have found his calling as an officer, said his father, Ronald Tate
"He had this enthusiasm, this fire in his soul," his father recalled.
That doesn't mean he didn't realize he was putting his life in danger by putting on a police uniform.
"He really knew the risk. But I think my son just thought people are generally good, and that's just the way he was," Ronald Tate said. "He thought people are generally good people, so let's treat them all with dignity."
A community mourns
The shooting marked the first time in 30 years that an officer was killed in the line of duty in Hattiesburg, Mayor Johnny DuPree told CNN.
"The men and women who go out every day to make sure that we are safe were turned on," DuPree said.
Mississippi Gov. Phil Bryant said he and his wife, Deborah, were mourning the officers' deaths.
"This should remind us to thank all law enforcement for their unwavering service to protect and serve," he said in a statement. "May God keep them all in the hollow of his hand."