She told police she had become concerned after spotting "pools of blood" on the bathroom floor.
The newborn was found inside the bathroom with a torn umbilical cord and a note.
Authorities have released photos of the woman they say left a newborn at the Tucson International Airport in January.
The woman then took the baby to the restroom outside the rental vehicle facility, where she left him with a handwritten note which read, "please help me".
'I just want what's best for him, and it is not me, ' the note reads.
The Tucson Airport Authority is searching for a woman who they believe abandoned a newborn at Tucson International Airport. She says the woman told her the naked baby was three months old. The custodian later found bloody clothes stuffed under paper towels in the trash can.
The child was in good condition, authorities said.
The note then switches to what appears to be a plea and apology from the mother.
All 50 USA states, Puerto Rico and Washington DC have a law known as the safe-haven or Baby Moses law which allows mothers to leave newborns at certain locations such as hospitals without fear of penalty. She can't and unfit to deal with me. The infant has now been handed over to the Arizona Department of Child Safety, the Washington Post quoted the airport police as saying.
Arizona is a "safe haven" state, meaning parents can drop off newborns at designated locations like staffed fire stations, hospitals, licensed adoption agencies, private welfare agencies and churches. Criminal charges have yet to be determined, the Arizona Daily Star reported, and the woman remains unidentified. "We would like to know who she is but we've exhausted our resources", an airport authority explained to the Washington Post. There are a lot of different things that are probably going through a mother's mind.