The Wisconsin Department of Justice has filed a petition asking for the full Seventh Circuit Court of Appeals to hear arguments in the case against Brendan Dassey.
The petition comes after a smaller panel of the court ruled in favor of a federal court's decision to overturn Dassey's conviction.
The state previously said that if the full court does not take the case or rules against the state, it would consider taking the case to the Supreme Court.
If the court is considering rehearing the case, it will call for a response from the defense within two weeks, according to the Wisconsin DOJ.
After a response is filed, the court takes about a month to decide whether to rehear the case.
The appeals court ruled last week that Dassey must stay in jail until the appeals process is finished.
Dassey was convicted of the 2005 murder of Teresa Halbach, along with his uncle, Steven Avery. Their story gained international attention when it was featured in the Netflix documentary "Making a Murderer."
A federal judge overturned his conviction last year, ruling investigators coerced Dassey into confessing. That decision was upheld by the Seventh Circuit Court of Appeals.