Custodian Juana Quintana told police she encountered the woman and asked if she was okay after seeing pools of blood on a bathroom floor. The baby was naked with its eyes closed, Quintana said, but the woman said the baby was 3 months old and left in a hurried manner.
Quintana said she found bloody clothes in the rubbish bin with paper towels on top in an apparent effort to conceal them.
The baby appeared healthy otherwise and was taken to a nearby hospital, airport spokeswoman Jessie Butler told the Washington Post. The baby is now in the custody of the Arizona Department of Child Safety, she said.
The airport authority also released photos of the scene and the handwritten letter found with the child.
"Please help me. My mom had no idea she was pregnant. She is unable and unfit to take care of me. Please get me to the authorities so they can find a good home," the message said, scrawled on notebook paper.
The note then switches to what appears to be a plea and apology from the mother.
The woman may have acted under assumption she was protected by regulations designed for new mothers to leave newborns with authorities without penalty.
The law, known as the safe-haven law or Baby Moses law, allows newborns to be left at designated areas like hospitals and firehouses to prevent the deadly practice of stranding unwanted babies. It applies in all 50 states, Puerto Rico and Washington, D.C., though states have differing regulations.
In 1999, Texas became the first state to pass a safe-haven law after reports of 13 abandoned babies in the Houston area in the first 10 months of the year, which prompted public outcry and legislative action, according to a Nevada state government review of the legal framework. The concept has roots in a similar series of abandoned babies in Alabama in 1998.
But the airports are not commonly designated as safe havens. 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," Butler told the paper. Airport police are not actively looking for the woman but will pursue any leads they receive.
In Arizona, babies must be under 72 hours old and unharmed to be legally abandoned, and has led to 40 rescues in the state and more than 3300 nationwide, the Arizona Safe Baby Haven Foundation says.
The group lists six hospitals in the state that have "drawers" where people can discreetly leave babies, though none are in Tucson. At one of the hospitals, Banner Thunderbird Medical Centre in Glendale, a drawer is connected to an internal alarm that alerts hospital staff of a dropped baby, according to a 2014 story by Raising Arizona Kids magazine.
"We hear stories where a baby is abandoned, or a mother who has had a baby doesn't know what to do, doesn't know who to turn to. There are a lot of different things that are probably going through a mother's mind. There is a lot of fear," said Kimberly Marshall, a nurse practitioner and co-founder of the Arizona Safe Baby Haven Foundation.