During a news conference on Saturday, a police spokesman said the family of Audrey Seiler is being very cooperative, but he did not get into details about what may happen next.
He also said it would be several days before a decision would be made about pressing criminal charges.
Audrey Seiler was reported missing on March 27 when a surveillance camera at her apartment building caught her leaving an exit without a coat or purse.
She was found four days later in a marsh two miles from her apartment.
Police called it abduction, but changed their minds when they began to discover inconsistencies in Seiler's story.
Last Friday she admitted to police that she faked the abduction and just wanted to be alone. Seiler and her family are not commenting about the case.