A Florida woman who cared for her disabled adult grandson on weekends faces second-degree murder charges after she told the police she gave him a fatal overdose over concerns about who would care for him when she died, the authorities said.

The police responded to a call on Sunday afternoon in Bradenton, Fla., about 40 miles south of Tampa, and found the grandson, Joel Parks, dead at the scene, Capt. Brian Thiers of the Bradenton Police Department said in a news conference on Tuesday. Mr. Parks was discovered by a sister.

Mr. Parks, 30, lived with his grandmother and part-time caretaker, Lillian Parks, 87, on weekends and in a group home during the week, Captain Thiers said. Mr. Parks was unable to care for himself, but details about his exact health condition were not known, he added.

After the authorities arrived, Ms. Parks made “several concerning remarks, spontaneous remarks,” including that she had “purposely overdosed” her grandson, Captain Thiers said.