Todd appeared before a city judge and waived her right to a hearing and was to be released from jail later Thursday.
Under the agreement, her criminal record will be expunged after if she stays out of trouble and gets mental treatment on probation. Most people spend a year on probation in the program, which is for first-time, nonviolent offenders.
"Our focus was really, 'This is somebody who appeared to have some mental issues,"' said prosecutor Chris Avetta. "And we wanted to make sure she doesn't hurt herself or anybody else."
Todd's public defender, Emily McNally, declined to comment.
Todd initially told investigators she was attempting to use a bank ATM on Oct. 22 when a 6-foot-4 black man approached her from behind, put a knife to her throat and demanded money. She told police she handed the assailant $60 and walked away.
Todd, who is white, told investigators she suspected the man then noticed a John McCain sticker on her car. She said the man punched her in the back of the head, knocked her to the ground and scratched a backward letter "B" into her face with a dull knife.
After admitting she made up the story, the woman told investigators she believed she cut the "B" onto her own cheek, but didn't remember doing so, police said last week.
She was charged with a misdemeanor count of making a false police report and had been jailed since Oct. 24. She underwent a court-ordered psychiatric examination and was deemed to be competent to stand trial, but in need of further counseling.
The charge Todd faced carries a maximum two-year jail sentence.
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