The police department also asked news outlets not to publicize the mother's hand-written note that officers had released Tuesday night in hopes of finding the mother.
Lt. Tom McLachlan said the department was concerned its investigation may discourage "future mothers" who may ponder giving up their newborn children.
Police, McLachlan said, would prefer a parent abandon an unwanted baby in a safe place, rather than dispose of it in a trash bin.
A mother on Saturday left her newborn in a West Valley City wardhouse of the Church of Jesus Christ of Latter-day Saints. The child, believed to be four or five days old, was wrapped in a blanket, with a note attached that asked the baby be taken care of.
The Utah Department of Child and Family Services has taken custody of the newborn.
Police released the note in the hope that someone would recognize the handwriting and provide tips about the mother.
Utah law allows mothers to abandon a child younger than 72 hours at a hospital. But the statute does not specifically apply to infants older than three days or to a child abandoned at places other than hospitals.
According to the law's sponsor, state Sen. Patrice Arent, parents who leave their children in a safe place to be cared for should be allowed to stay anonymous. Pursuing a parent, such as the one who left the boy in West Valley, could create a chilling effect, said Arent, a Democrat from Murray.
"The bottom line is we applaud her for making sure the baby was safe and the baby was important," Arent said.

