The pleas were sent by fax to suburban Rocky River Municipal Court by their attorneys.
The faxed pleas included a request that a requirement that the couple appear in person for a June 19 arraignment be dropped.
Police said they were tipped off by postal inspectors to suspicious packages mailed to the Perez home and arranged a delivery last Tuesday under surveillance. Police say Melanie Perez accepted two packages.
Authorities say Melanie Perez, whose maiden name is Baum, told the undercover officer delivering the packages that they were intended for her dog, named Brody. The package was addressed to Brody Baum.
According to investigative reports, Perez told drug agents with a search warrant that he had pot for personal use and pointed out two jars. Asked about any drugs or weapons by officers who went to the Perez home, Perez "volunteered to direct the officers to the location of it," an investigative report said.
The 27-year-old Perez and his 29-year-old wife were charged Friday with misdemeanour drug possession involving just over one-third of a pound of marijuana. Perez and his wife were released on personal bond.
Outside legal experts say the charge typically is handled like a traffic ticket and might result in a fine.
Under the drug agreement between Major League Baseball and its players' association, marijuana offences generally result with the player undergoing a treatment program rather than discipline.
Perez has six saves this season but is on the disabled list with an injured right shoulder.