Convicted murderer Jane Andrews went on the run from East Sutton Park near Maidstone on Sunday, four days after being transferred from another open prison in Surrey.
The women-only facility was amalgamated with Blantyre House in 2007 and is run by the same governor, Jim Carmichael.
While staff at all-male Blantyre declined to comment on the incident this week, a spokesman for HM Prisons Service confirmed it was not felt procedures at either site needed to be examined as a result.
The spokesman said: "There wasn't a breach of security.
"Prisoners are rigorously risk assessed and categorised as being of low risk to the public before being placed in open conditions.
"For long-term prisoners, these are essential components for successful resettlement and an important factor in protecting the public."
A 42-year-old former aide to the Duchess of York, Andrews was sentenced to a minimum 15 years in jail for killing her boyfriend when he refused to marry her in 2001.
She was recaptured early on Wednesday after police found her in a Maidstone hotel room, and will return to a closed prison.