SCOTUS seized that power in Marbury v Maddison. However, the Constitution itself is at best unclear on the issue.
In Marbury v Madison, Justice Marshall and SCOTUS rightly claimed the constitutional power of judicial review of legislative acts. (What invalidated the ruling was that SCOTUS did not have original jurisdiction in the case and should have dismissed the case out of hand. Nevertheless, the ruling stands and is an accurate assessment of constitutional judicial power).
The Court in Marbury v. Madison, however, does not rule against the power of the states to declare a federal act unconstitutional. The ruling does not directly address this issue at all. However, in correctly characterizing the Constitution, the ruling gives weight to the inherent power of the states to rule against either unconstitutional federal legislation or rulings.
The powers of the Legislature are defined and limited; and that those limits may not be mistaken or forgotten, the Constitution is written. To what purpose are powers limited, and to what purpose is that limitation committed to writing, if these limits may at any time be passed by those intended to be restrained?...[T]he theory of every such government must be that an act of the Legislature repugnant to the Constitution is void…From these and many other selections which might be made, it is apparent that the framers of the Constitution contemplated that instrument as a rule for the government of courts, as well as of the Legislature. Marbury v Madison, 5 U.S. (1 Cranch) at 176, 177, 179-80.
http://www.law.cornell.edu/supremecourt/text/5/137#writing-USSC_CR_0005_0137_ZO