This is not exactly true. The restriction in question is the Fourth Amendment, which generally protects citizens from unreasonable searches and seizures --- agents of the state have to obtain a search warrant from a judge before they can search private property.
In general in the last century the Supreme Court has interpreted the Fourteenth Amendment as "incorporating" the Bill of Rights. Although the Bill of Rights was originally written to apply specifically to the federal government, the Due Process clause of the 14th Amendment has been read as applying these protections to state governments as well.
In particular, in Mapp v. Ohio in 1961 the Supreme Court held that under the Due Process clause the Fourth Amendment's prohibition of arbitrary search and seizure applies to state governments as well.
In general in the last century the Supreme Court has interpreted the Fourteenth Amendment as "incorporating" the Bill of Rights. Although the Bill of Rights was originally written to apply specifically to the federal government, the Due Process clause of the 14th Amendment has been read as applying these protections to state governments as well.
In particular, in Mapp v. Ohio in 1961 the Supreme Court held that under the Due Process clause the Fourth Amendment's prohibition of arbitrary search and seizure applies to state governments as well.