A Question of Differences
ERRATA: It does not appear as if there are state laws that require babies to be born in hospitals. I had been told there were, long ago, by someone I trusted to know what they were talking about. However, on the topic of infanticide, you could consider the (passed in 2005) Born Alive Infant Protection Act.
Alexander Hamilton wanted laws on this to be easier, so that women could retain their dignity, and hope to join polite society. At least according to Richard Brookhiser's book "What Would the Founders Do?" Link from Google Books. Section begins "As a politician, Hamilton spoke up for single mothers." and ends with "Morris married an unwed mother because he thought for himself."