District Attorney Brent Cooper tells news outlets Tad Cummins takes medicine to control his blood pressure and likely will need a refill.
Cummins and 15-year-old Elizabeth Thomas were reported missing on March 13.
The last confirmed sighting of the pair was two days later at an Oklahoma City Wal-Mart. Police have issued an Amber alert for Thomas and say they have warrants charging Cummins with sexual contact with a minor and aggravated kidnapping.
Cooper also said Cummins left a note for his wife before disappearing, but officials think it was a diversion to mislead the investigation.