She later allegedly shot and killed Peter Ndwiga Njiru, 32, in a lodging in Juja, Kiambu county, about 200 kilometres from the scene where she killed the police officer.
The senior officers are afraid as they don’t know who her next target could be.
Kangogo is also said to have sent a threatening message to her former husband, before fleeing Nakuru.
This has prompted fears among many officers who were close to her that she could knock on their door.
The police have had a major headache tracing her movements as she abandoned her phone at the scene of the first shooting.
There were reports on Tuesday evening that she had surrendered in Nakuru, but this turned out to be false. Police sources told the Star that security agencies believe she could have been behind the false report.
What is puzzling to authorities is the fact that she is using a single bullet on her victims, and she is armed with a stolen pistol with 14 bullets.
Director of Criminal Investigations George Kinoti appealed to the public to help them apprehend the woman whom he termed ‘rogue, armed and dangerous’.
Kangogo has served at various police stations, including Railways command, before she was posted to Nakuru, where she has been for almost three years.
“We don’t know if she intends to use a single bullet on her victims before she is caught or what her next plans are,” a senior officer, who revealed there were fears among many units and officers, said.
Police said the officer, who took off with Ogweno’s firearm, a loaded Ceska pistol, lured a man to a guest house in Kimbo, Juja, at around 4pm on Monday.
She later emerged from the room at around midnight on Monday and fled, leaving Njiru’s blood-soaked body sprawled on the bed.
Detectives have established that she lured the man to the room after paying for it. She shot him in the head at point-blank.
She told an attendant working at the guest house that she had gone to buy toothpaste. Kangogo did not return.