Gonzalez's attorney Matt Morgan told ABCNews.com on Jan. 8 that it was "critical" to their case because, "At this junction, we have been unable to get testimony from Casey Anthony...because she has been hiding behind the shield of the fifth amendment."
Anthony's appeal on the criminal charge allowed her to plead the fifth so that she does not incriminate herself in her criminal case.
If the state does not appeal to the Supreme Court, Anthony could eventually be forced to answer questions about Caylee in the civil trial.
"We expect that her criminal appeal will hopefully be resolved and she will no longer have protection for the fifth amendment to hide behind," Morgan said.
Morgan hopes that the civil trial will be able to proceed in the late spring or early summer.
Anthony completed her one-year probation for check fraud in August, leaving her free to go wherever she pleases. She resurfaced a few times over the past year via a leaked video diary and a telephone conversation with Piers Morgan, but has otherwise succeeded in disappearing from the public eye.