(CNN) -- The father of three missing Michigan boys has no "established relationship" with a mystery woman that he claimed he left his sons with before unsuccessfully trying to commit suicide, a police chief investigating the boys' disappearance said Monday.
John Skelton, the father, told police that he dropped the boys off Friday morning with a woman he identified as Joann Taylor, in part to ensure that they did not witness his suicide.
Authorities said Skelton's suicide attempt was not successful, and he is being held at a mental health facility.
"There is no established relationship between he and the person that he described to us as Joann Taylor," Chief of Morenci Police, Larry Weeks, told reporters.
The police chief asked for the public's help with information regarding Skelton's blue 2000 Dodge Caravan, later discovered by police, that was believed to be carrying the boys between 2:30 p.m. Thursday to 1:30 p.m. Friday.
Skelton told police that Taylor was supposed to take the boys to the boy's home in Morenci, a southern Michigan town of about 2,400 people about 40 miles west-northwest of Toledo, Ohio, around 3 p.m. Friday.
But the boys -- 5-year-old Tanner Skelton, 7-year-old Alexander William Skelton and 9-year-old Andrew Skelton -- never arrived and police aren't sure whether John Skelton's story is true. They say they don't know whether Taylor is real.
"We remain hopeful," Weeks said Monday. "That's why we're doing what we're doing, and hope to bring these boys home."
Authorities issued an Amber Alert on Friday. The last nonfamily member saw the boys at 5 p.m. on Thursday, according to the chief.
The alert notes that Tanner is 3 feet, 6 inches tall, has strawberry blond hair, blue eyes and weighs about 40 pounds. Alexander is 3 feet, 9 inches tall, has brown hair and eyes, weighs about 45 pounds and has scars on his hairline and chin. The oldest brother, Andrew, is 4 feet, 1 inch tall, has brown hair and eyes and weighs roughly 57 pounds.
Kathye Herrera, a family spokeswoman, spoke to reporters Sunday, thanking neighbors who have searched for the boys and prayed for their safe return.
"We've got three great little boys out there, and we're going to get them back," she said.
Authorities asked the public Sunday for help in locating three young boys missing for several days.
"We need calls. We need tips. Anything that's out there, no matter how incredible you may think it is, call. Let us know," said Andy Arena, a special agent with the FBI.