Any alien who... (3) attempts to enter or obtains entry to the United States by a willfully false or misleading representation or the willful concealment of a material fact, shall, for the first commission of any such offense, be fined under title 18 or imprisoned not more than 6 months, or both, and, for a subsequent commission of any such offense, be fined under title 18, or imprisoned not more than 2 years, or both.

Marriage fraud:

Any individual who knowingly enters into marriage for the purpose of evading any provision of the immigration laws shall be imprisoned for not more than 5 years, or fined not more than $250,000, or both.

New York State Consolidated Laws–Penal(http://caselaw.lp.findlaw.com/nycodes/c82/a65.html)

Article 260 – Offenses Relating to Children, Disabled Persons and Vulnerable Elderly Persons

Section 260.05-- Non-support of a child in the second degree

A person is guilty of non-support of a child when, being a parent, guardian or other person legally charged with the care or custody of a child less than sixteen years old, he fails or refuses without lawful excuse to provide support for such child when he is able to do so, or becomes unable to do so, when, though employable, he voluntarily terminates his employment, voluntarily reduces his earning capacity or fails to diligently seek employment.

Non-support of a child in the second degree is a Class A misdemeanor.

Article 255 -- Offenses Affecting the Marital Relationship(http://caselaw.lp.findlaw.com/nycodes/c82/a64.html)

Section 255.15 – Bigamy

A person is guilty of bigamy when he contracts or purports to contract a marriage with another person at a time when he has a living spouse, or the other person has a living spouse.

Bigamy is a Class E felony

Article 175 – Offenses Involving False Written Statements(http://caselaw.lp.findlaw.com/nycodes/c82/a40.html)

Section 175.30 -- Offering a false instrument for filing in the second degree

A person is guilty of offering a false instrument for filing in the second degree when, knowing that a written instrument contains a false statement or false information, he offers or presents it to a public office or public servant with the knowledge or belief that it will be filed with, registered or recorded in or otherwise become a part of the records of such public office or public servant.

Offering a false instrument for filing in the second degree is a Class A misdemeanor.

Section 175.35 -- Offering a false instrument for filing in the first degree

A person is guilty of offering a false instrument for filing in the first degree when, knowing that a written instrument contains a false statement or false information, and with intent to defraud the state or any political subdivision, public authority or public benefit corporation of the state, he offers or presents it to a public office, public servant, public authority or public benefit corporation with the knowledge or belief that it will be filed with, registered or recorded in or otherwise become a part of the records of such public office, public servant, public authority or public benefit corporation.

Offering a false instrument for filing in the first degree is a Class E felony.