Blane Barksdale, 56, and Susan Barksdale, 59, broke free from two guards on Monday evening.
They escaped from Blanding, a rural town in southeast Utah, the Tuscon Police Department said in a statement.
The couple are wanted in connection with the murder of Frank Bligh, 72, in Tuscon, Arizona, in April this year.
Police warned that they are considered armed and dangerous.
The couple were being extradited from the New York town of Henrietta, where they were arrested in May, to Prima County, Arizona, to face a murder charge, police said.
They were last seen driving a red GMC Sierra pickup truck, with damage to the front passenger side and rear bumper.
Their direction of travel is currently unknown, though investigators believe they are travelling through Arizona.