@jca It varies from state to state. In some states, they can do it without anything happening. They can even do it anonymously. From the information below, it sounds like, while NY can serve people for neglect, the fact that they did it though the safe haven actually makes it so that they don’t actually get in trouble for it (since it’s an affirmative defense in NY).
From this site “In approximately 12 States, anonymity for the parent or agent of the parent is expressly guaranteed in statute. In 24 States and Puerto Rico, the safe haven provider cannot compel the parent or agent of the parent to provide identifying information. In addition, 13 States provide an assurance of confidentiality for any information that is voluntarily provided by the parent.
In addition to the guarantee of anonymity, most States provide protection from criminal liability for parents who safely relinquish their infants. Approximately 33 States (Alaska, Arizona, California, Connecticut, Florida, Georgia, Hawaii, Idaho, Illinois, Iowa, Kansas, Kentucky, Louisiana, Maryland, Massachusetts, Minnesota, Missouri, Montana, Nevada, New Mexico, North Carolina, North Dakota, Ohio, Oklahoma, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Vermont, Washington, and Wisconsin) and Puerto Rico do not prosecute a parent for child abandonment when a baby is relinquished to a safe haven. In 16 States, safe relinquishment of the infant is an affirmative defense in any prosecution of the parent or his/her agent for any crime against the child, such as abandonment, neglect, or child endangerment.
The privileges of anonymity and immunity will be forfeited in most States if there is evidence of child abuse or neglect.”
From the link I provided, it says that, “In a State with an affirmative defense provision, a parent or agent of the parent can be charged and prosecuted, but the act of leaving the baby safely at a safe haven can be a defense to such charges. The States with an affirmative defense provision include Alabama, Arkansas, Colorado, Delaware, Indiana, Maine, Michigan, Mississippi, Missouri, New Jersey, New York, Oregon, Utah, Virginia, West Virginia, and Wyoming”. (emphasis mine)
This link covers the above information and then goes on to break it down state by state for anyone interested. It took a while to load for me, so be warned that it might be slow.