Complicating the search is the fact that police aren't sure whether the father, John Skelton, 39, is telling the truth about the last time he saw his sons, reports CNN.
Skelton – who is now recuperating in an Ohio mental health facility – reportedly told investigators he dropped the boys (9-year-old Andrew, 7-year-old Alexander and 5-year-old Tanner) off Friday morning with a woman by the name of Joann Taylor, whom he allegedly met online.
Taylor, he says, was to take the boys home to their mother, Tanya Skelton, so that they would not witness his attempt to hang himself (Tanya and John Skelton are separated).
Police, however, have not yet been able to determine whether Taylor even exists. And the boys never arrived at their mother's home.
Tanya Skelton is said to be serving as a "valuable resource" to the investigation, Police Chief Larry Weeks told reporters.
In the meantime, authorities have issued an Amber Alert for the boys, last seen by a non-family member on Thursday. And Morenci residents are searching parks and creeks in the area, about 75 miles southwest of Detroit.