Lucinda Moyers, 56, will not be facing a three strikes charge that could have sent her to prison for 25 years.
The District Attorney reportedly doesn't think the nature of her prior offenses calls for it.
Records show Moyers has been convicted of four burglaries since 1990.
Authorities said she broke into Trebek's room on July 26 and stole a bracelet, purse and wallet.
Trebek said he tore his Achilles tendon as he tried to chase her.