The officers roughed up the suspected and locked her up at the camp before being moved to Muthangari Police Station.
This was after angry members of the public thronged the camp baying for the suspect's blood.
Police have arrested a suspect in connection with the theft of a twin boy from Kenyatta National Hospital on Sunday morning.
It is a dramatic twist to a story that has captured the imagination of Kenyans, resulting in an outpouring of online messages of support for the affected parents Job Ouko and Jane Kerubo.
The suspect, who is yet to be identified, was arrested after a concerned individual called Mr Ouko with news about the sighting of the baby and the woman in Kawangware.
Mr Ouko then contacted the area chief who accompanied him to the residential block where the suspect had been spotted.