Murphy and her attorney, Rick Santwier, would not comment on the case or the plea agreement outside of court.
In the courtroom, Murphy softly replied "guilty" when asked her plea to the charges.
Her only other responses were "yes" when asked by Krag if she understood the charges against her, the conditions of her agreement and penalties if she didn't meet the requirements of the agreement.
Murphy is scheduled to return to court Feb. 22 with proof that she has enrolled in a drug program, which she must complete within 18 months and parenting classes she must complete within five years.
Failure to complete the drug program could result in a prison term of up to three years; and failure to complete the parenting classes could result in up to six months in jail, Krag said.
Burbank City Manager Mary Alvord said the plea puts an end to a difficult chapter for the city.
"For all of us, and for her, it's good to get this behind us," Alvord said.
Glendale City Councilman Dave Weaver had minimal contact with Murphy when she was serving in Burbank but still wished her well now that the case had ended.
"It couldn't have been easy on her or her family," Weaver said. "You want to get something like that behind you. It's good for her and the community."
Burbank Councilwoman Marsha Ramos declined to comment specifically on Murphy's plea but commended the Burbank Police Department for their level of professionalism in handling the case.
"I think they should feel satisfied with their work," Ramos said. "It's the reality of police work to stop violence, drugs and guns in our community."
Burbank Police supported the district attorney's office in the conclusion the case, Burbank Police spokesman Sgt. Jay Jette said.
"The guilty plea supports the facts in the case," Jette said.