Waiters who served Maj-Gen (Rtd) Joseph Nkaissery at the Bomas of Kenya bar are among people being interviewed over the death of the powerful internal security Cabinet secretary.
Director of Criminal Investigations Ndegwa Muhoro also revealed on Sunday that police bodyguards assigned to the CS were also being questioned by detectives pursuing a line of sudden death.
"According to the Criminal Procedure Code, sudden death must be investigated, even if it was sicknesses or accident," Mr Muhoro said.
Even though he appeared to rule out foul play in the death on Saturday night of the tough-talking CS, he said a postmortem examination scheduled for Monday is key to the investigation.
"We are looking into it but the postmortem will determine the direction of the investigations," Mr Muhoro said.
"The law requires that sudden death must be investigated.
"Not that we suspect anything, but we have to deal with the law. Any person who had contact with him must be questioned. Naturally, that is the course of the investigation."
The CS was, besides President Uhuru Kenyatta and his deputy William Ruto, the most-guarded government officer in Kenya.
Independent sources said Mr Nkaissery's family had appointed a pathologist, who is expected to work with the government's own, during the autopsy.
"We are working closely with the family because, according to the criminal procedure code, there must be an inquest. Postmortem is key," Mr Muhoro said.
"Not that we are suspecting foul play. Even sports people have died on the pitch. Until postmortem is done, we don't need speculation. The law says we must investigate."
He went on: "Anybody who was at work, anybody who was in contact with him, must be questioned."
Speaking at the late minister's home in Karen, Nairobi, former military chief Jeremiah Kianga urged investigators to move quickly and let Kenyans know the cause of death.
"They should do so quickly and make public the reason behind the death," Gen (Rtd) Kianga said.
At a prayer service at the home, former Narok North MP Moses ole Marima said Mr Nkaissery's widow Hellen had said the CS fell in his house when he tried to get out of bed.
"I talked to his wife, who said she heard him wake up at night and slump on the floor," Mr Marima said.
Head of Public Service Joseph Kinyua had on Saturday said the CS died at The Karen Hospital shortly after he arrived for a check-up, but a second statement by Government Spokesman Eric Kiraithe said the death occurred at home.
"Details related to his sudden death are now beginning to emerge," Mr Kiraithe said in a statement.
"It is now clear that the general collapsed while at home and was rushed to The Karen Hospital and, upon further examination, was pronounced dead on arrival.
"Both the hospital and his family have clarified that he was not admitted at the facility.
"Under the strenuous circumstances, an earlier statement indicating that Nkaissery passed on while receiving treatment at The Karen Hospital was made in error."
The chairman of the Karen Hospital Board, Dr James Mageria, said the CS was dead by the time he was received at the facility.
"He was already dead, I can confirm to you that. It was too late since he was already gone," Dr Mageria told Nairobi News.
He added: "I am the one who called top government officers, including Kinyua, the Inspector-General of Police Joseph Boinnet and CID Director Ndegwa Muhoro to the hospital and handed over the body to them and Nkaissery's family members."
The bar has since been sealed off with a police yellow tape, indicating it is a scene of crime.
The Nation established that the first to arrive at the hospital was the Deputy Inspector-General in charge of Kenya Police Joel Kitili, followed by Mr Boinnet.