Complex sentence: Strictly speaking, neither the U.S. Supreme Court Library nor the Law Library of Congress is a public access law library; both, however, are government libraries funded by taxpayers, and accountable to the U.S. Supreme Court or to the U.S. Congress respectively.
Split into simpler sentences: Strictly speaking, neither the U.S. Supreme Court Library nor the Law Library of Congress is a public law library. Both, however, are government libraries funded by taxpayers, and accountable to the U.S. Supreme Court or to the U.S. Congress respectively.