(CNN) -- Police and neighbors were searching for three young Michigan boys Saturday who have been missing since their father claimed he dropped them off with a woman before trying to kill himself a day earlier.

The father survived his suicide attempt and is being cared for in a mental health facility, said Morenci, Michigan, Police Chief Larry Weeks on Saturday.

But Michigan authorities do not know what has happened to his boys -- 5-year-old Tanner Skelton, 7-year-old Alexander William Skelton and 9-year-old Andrew Skelton -- prompting them to issue an Amber Alert on Friday.

Weeks said that the boys' father, John Skelton, told police that he dropped the boys off Friday morning with a woman he identified as Joann Taylor -- in part to ensure they didn't see him while and after he tried to commit suicide.

John Skelton told police that the woman, whom he allegedly met on the internet, was supposed to drop the boys off at their home in Morenci, a southern Michigan town of about 2,400 people about 40 miles west-northwest of Toledo, around 3 p.m. Friday.

But the boys never went home and, Weeks added, authorities still aren't sure if John Skelton's story -- including Joann Taylor's existence -- is true or a fabrication.

"We have not been able to locate a Joann Taylor or confirm that she even exists," Weeks told reporters Saturday evening.

The last non-family member saw the boys at 5 p.m. on Thursday, according to the chief.

Their mother, Tanya, has been with police "virtually the entire day" on Saturday, answering questions and serving as what Weeks called a "valuable resource at this time."

Weeks said Tanya Skelton had "contact with someone alleging to be Joann," adding only that this communication was not necessarily by phone or in person.

According to the Amber Alert, Taylor may have been from Jackson or Hillsdale counties and may be driving a silver van. Still, Weeks reiterated that they have yet to confirm she is real and, if so, if she is with the boys.

Saturday's press conference was crowded with media and residents of Morenci, many of whom have been searching for the young boys. Dozens spent Saturday searching along Bean Creek, Wakefield Park and the Riverside Natural Area -- all in Morenci -- according to Toledo-based CNN affiliate WUPW.

"We just hope they're somewhere safe and warm playing video games," volunteer Carol Garcia told WUPW.

But authorities thus far have offered few tips pointing community members to places where the young Skeltons might be.

"We understand their drive and desire to be out there," said Weeks. "The fact is, I cannot tell the community there's a specific location they should be searching."

The alert notes that Tanner is 3 feet, 6 inches tall, has strawberry blond hair, has 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.