No. The US Supreme Court can nullify a challenged state law if it conflicts with the federal Constitution.
A state's legislature can nullify its own laws. A state cannot nullify a federal law, as the Constitution shall be "the supreme law of the land".
Any court can declare a law unconstitutional, but the government would appeal the decision to the US Supreme Court, the ultimate arbiter of constitutionality. Due to the appeals process, only the Supreme Court nullifies federal (and sometimes state) laws.
State courts interpret state laws, and state supreme courts interpret state constitutions.
The US Supreme Court only has limited power over the state courts because state laws and state constitutional issues that aren't in conflict with the US Constitution lay outside the Supreme Court's jurisdiction.
The US Supreme Court can nullify state laws that conflict with the federal constitution. While the Court has jurisdictional limitations, they are not accurately described by the question.
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Supreme Court to declare acts of Congress and state laws unconstitutional
State constitutions The United States judiciary consists of parallel systems of federal and state courts. Each of the 50 states has its own system of courts whose powers derive from state consitutions and laws. The federal court system consists of the Supreme Court and lower federal courts established by Congress. Federal courts derive their powers from the Constitution and federal laws.
Each state has its own court system. These courts are created by state statute or constitution to enforce state civil and criminal laws. Most of the states have trial courts, intermediate courts of appeal, and a supreme court.
It is usually the US Supreme Court that can block a federal law. State Supreme Courts block states' laws. They can do this if the law is deemed unconstitutional or is in conflict with rights already protected in other laws.
The state court system deals with state laws; however, the federal court system may also hear cases involving state laws under certain conditions.
The Supreme Court of the United States for federal law and US constitutional issues or the equivalent in the state court systems for matters involving state and municipal laws and state constitutional issues. While most state courts of final appeal are called [State name] "supreme court," a few courts use other designations. For example, in New York the high court is called the New York State Court of Appeals.