what law (federal, state,etc) does abortion fall under?

Abortion laws are state laws.

http://www.ncsl.org/issues-research/health/abortion-laws.aspx

what is the law in regards to new york

http://www.safestabortion.com/in-the-know/abortion-laws/

http://statelaws.findlaw.com/new-york-law/new-york-abortion-laws.html

Abortion laws in the United States are primarily regulated at both the federal and state levels. The primary federal law regarding abortion is the landmark Supreme Court decision made in 1973, known as Roe v. Wade. This ruling legalized abortion across the country. However, it is important to note that subsequent court decisions, as well as federal and state legislation, have imposed certain limitations on the practice of abortion.

In addition to federal law, each state has the power to regulate abortion within its own jurisdiction. This means that while Roe v. Wade ensures the right to abortion, states can still impose specific restrictions, such as mandatory waiting periods, parental consent requirements, gestational limits, or licensing requirements for providers.

To determine the specific abortion laws in a particular state, it is necessary to consult the statutes and regulations of that state. These laws can be accessed through official government websites, such as state legislative websites or websites maintained by relevant state agencies.

Please note that abortion laws can vary significantly from state to state, so it is essential to refer to the specific laws of the state in question for accurate and up-to-date information.