For purposes of criminal law, in practice, airports in the United States are treated as part of the territory of the state (or district or territory) that they are a part of and of the United States. The scope of maritime criminal jurisdiction is defined at 18 USC 7. It states:
The term “special maritime and territorial jurisdiction of the United
States”, as used in this title, includes:
(1) The high seas, any other waters within the admiralty and maritime
jurisdiction of the United States and out of the jurisdiction of any
particular State, and any vessel belonging in whole or in part to the
United States or any citizen thereof, or to any corporation created by
or under the laws of the United States, or of any State, Territory,
District, or possession thereof, when such vessel is within the
admiralty and maritime jurisdiction of the United States and out of
the jurisdiction of any particular State.
(2) Any vessel registered, licensed, or enrolled under the laws of the
United States, and being on a voyage upon the waters of any of the
Great Lakes, or any of the waters connecting them, or upon the Saint
Lawrence River where the same constitutes the International Boundary
Line.
(3) Any lands reserved or acquired for the use of the United States,
and under the exclusive or concurrent jurisdiction thereof, or any
place purchased or otherwise acquired by the United States by consent
of the legislature of the State in which the same shall be, for the
erection of a fort, magazine, arsenal, dockyard, or other needful
building.
(4) Any island, rock, or key containing deposits of guano, which may,
at the discretion of the President, be considered as appertaining to
the United States.
(5) Any aircraft belonging in whole or in part to the United States,
or any citizen thereof, or to any corporation created by or under the
laws of the United States, or any State, Territory, district, or
possession thereof, while such aircraft is in flight over the high
seas, or over any other waters within the admiralty and maritime
jurisdiction of the United States and out of the jurisdiction of any
particular State.
(6) Any vehicle used or designed for flight or navigation in space and
on the registry of the United States pursuant to the Treaty on
Principles Governing the Activities of States in the Exploration and
Use of Outer Space, Including the Moon and Other Celestial Bodies and
the Convention on Registration of Objects Launched into Outer Space,
while that vehicle is in flight, which is from the moment when all external doors are closed on Earth following embarkation until the
moment when one such door is opened on Earth for disembarkation or in
the case of a forced landing, until the competent authorities take
over the responsibility for the vehicle and for persons and property
aboard.
(7) Any place outside the jurisdiction of any nation with respect to
an offense by or against a national of the United States.
(8) To the extent permitted by international law, any foreign vessel
during a voyage having a scheduled departure from or arrival in the
United States with respect to an offense committed by or against a
national of the United States.
(9) With respect to offenses committed by or against a national of the
United States as that term is used in section 101 of the Immigration
and Nationality Act— (A) the premises of United States diplomatic,
consular, military or other United States Government missions or
entities in foreign States, including the buildings, parts of
buildings, and land appurtenant or ancillary thereto or used for
purposes of those missions or entities, irrespective of ownership; and
(B) residences in foreign States and the land appurtenant or ancillary
thereto, irrespective of ownership, used for purposes of those
missions or entities or used by United States personnel assigned to
those missions or entities. Nothing in this paragraph shall be deemed
to supersede any treaty or international agreement with which this
paragraph conflicts. This paragraph does not apply with respect to an
offense committed by a person described in section 3261(a) of this
title.
Often, law enforcement at an international airport is provided by a county sheriff or municipal police department in addition to the TSA (including air marshalls) which has narrower jurisdiction, in contrast to places like Indian Reservations and federal parks, which while within a state are outside state and local law enforcement jurisdiction (although the assimilative crimes act applies state law in many such circumstances). They are definitely not subject to maritime jurisdiction in the United States.
