The filing asks a higher court to consider whether the arrest warrant is even valid.
Quintana Roo state prosecutor Rodolfo Garcia says the petition arrived Friday.
Beresford-Redman is charged with killing his wife, Monica, while the two vacationed at a Cancun resort in April.
He denies the charges.
His lawyers said Thursday that he would surrender to U.S. authorities if necessary, but he intends to fight extradition.
The Associated Press contributed to this report.
