The 1967 referendum gave the federal Parliament the power to make laws for Aboriginal Australians. Prior to 1967, section 51 of the Australian Constitution, which outlines the law-making powers of the federal Parliament, stated that the Parliament could make laws with respect to 'people of any race, other than the Aboriginal race in any state'. Before this the states, rather than the federal government, had responsibility for Aboriginal affairs.
Today, state parliaments can still make laws for Aboriginal Australians; however if these laws conflict with laws made by the federal Parliament the state law will be overridden. This is because under section 109 of the Constitution if the federal Parliament and a state parliament pass conflicting laws on the same subject, the federal law overrides the state law.
For more information about the law-making powers of the three levels of government, click here.