The 40-year-old lawyer, who works in Canterbury, was detained on 18 June. A CPS spokesman said the arrest was not connected to her work.
The lawyer, from Dover, was released on bail pending further inquiries after questioning by police at Tonbridge.
Kent Police said it was collaborating closely with the CPS in the matter.
The CPS spokesman said: "A CPS lawyer from another division is considering the evidence submitted by the police."