No charges have been filed and the matter remains under investigation. A message seeking comment was left for Perez's attorney.
At a news conference Wednesday, the chief said the operation likely originated with a package that appeared suspicious to postal employees. "They took it from there," he said.
In a brief written update Wednesday afternoon, the chief confirmed the shipment was suspected to be marijuana, but said that the state crime laboratory will have to confirm that.
"Depending on what it was and how much it was, charges will be filed accordingly," Stillman said.
Officers with a search warrant took evidence from the Perez house, according to the chief, but the seized items weren't specified.
Indians general manager Chris Antonetti said in a statement that the team had talked with Perez and was "gathering additional information."
Manager Terry Francona, addressing the situation before the Indians' Wednesday afternoon game against the Yankees in New York, said he had reached out to Perez to check on him.
"I spoke to him this morning, called him, just wanted to make sure he was OK," he said. "Out of respect to everybody involved, that's really all I can say."
The Indians' often-polarizing closer has six saves this season, but is on the disabled list with an injured right shoulder. He and Cleveland fans have gotten on each other's nerves over the last couple years, and he recently deactivated his Twitter account after hearing it from fans following a couple of bad outings.
In previous seasons, Perez has criticized fans for not coming to games, and ownership for not spending money on free agents.
The right-hander was supposed to start throwing again this week. Francona said he wasn't sure if the investigation would affect Perez' injury rehabilitation.
"I don't know. I honestly don't know," he said. "Let's not only go one day at a time, let's go one hour at a time here."