The Australian Constitution recognises Government at Federal

Federal government

The federal government is the common government of a federation. The structure of federal governments varies from institution to institution. Based on a broad definition of a basic federal political system, there are two or more levels of government that exist within an established territory and...

 and State

State government

A state government is the government of a subnational entity in a federal form of government, which shares political power with the federal or national government. A state government may have some level of political autonomy, or be subject to the direct control of the federal government...

 levels, but makes no mention of local government

Local government

Local government refers collectively to administrative authorities over areas that are smaller than a state.The term is used to contrast with offices at nation-state level, which are referred to as the central government, national government, or federal government...

. Constitution Alteration (Local Government) 1988 proposed to alter the constitution so as to recognise local government. The proposal was put to a referendum in the Australian referendum, 1988

Australian referendum, 1988

The 1988 Australian Referendum was held on 3 September 1988. It contained four referendum questions, none of which passed. The failure was generally attributed to the open ended and nondescriptive wording of the proposed amendments....

.

Results

A Proposed Law: To alter the Constitution to recognise local government.

Do you approve this proposed alteration?

Result

State	On rolls	Ballots issued	For		Against		Informal
				%		%
New South Wales New South Wales New South Wales is a state of :Australia, located in the east of the country. It is bordered by Queensland, Victoria and South Australia to the north, south and west respectively. To the east, the state is bordered by the Tasman Sea, which forms part of the Pacific Ocean. New South Wales...	3,564,856	3,297,246	1,033,364	%31.70	2,226,529	%68.30	37,353
Victoria	2,697,096	2,491,183	882,020	%36.06	1,563,957	%63.94	45,206
Queensland Queensland Queensland is a state of Australia, occupying the north-eastern section of the mainland continent. It is bordered by the Northern Territory, South Australia and New South Wales to the west, south-west and south respectively. To the east, Queensland is bordered by the Coral Sea and Pacific Ocean...	1,693,247	1,542,293	586,942	%38.31	945,333	%61.69	10,018
South Australia South Australia South Australia is a state of Australia in the southern central part of the country. It covers some of the most arid parts of the continent; with a total land area of , it is the fourth largest of Australia's six states and two territories.South Australia shares borders with all of the mainland...	937,974	873,511	256,421	%29.85	602,499	%70.15	14,591
Western Australia Western Australia Western Australia is a state of Australia, occupying the entire western third of the Australian continent. It is bounded by the Indian Ocean to the north and west, the Great Australian Bight and Indian Ocean to the south, the Northern Territory to the north-east and South Australia to the south-east...	926,636	845,209	247,830	%29.76	584,863	%70.24	12,516
Tasmania Tasmania Tasmania is an Australian island and state. It is south of the continent, separated by Bass Strait. The state includes the island of Tasmania—the 26th largest island in the world—and the surrounding islands. The state has a population of 507,626 , of whom almost half reside in the greater Hobart...	302,324	282,785	76,707	%27.50	202,214	%72.50	3,864
Australian Capital Territory Australian Capital Territory The Australian Capital Territory, often abbreviated ACT, is the capital territory of the Commonwealth of Australia and is the smallest self-governing internal territory...	166,131	149,128	58,755	%39.78	88,945	%60.22	1,428
Northern Territory Northern Territory The Northern Territory is a federal territory of Australia, occupying much of the centre of the mainland continent, as well as the central northern regions...	74,695	56,370	21,449	%38.80	33,826	%61.20	1,095
Total for Commonwealth	10,362,959	9,537,725	3,163,488	%33.61	6,248,166	%66.39	126,071
Obtained majority in no State and an overall minority of 3 084 678 votes.
Not carried

Discussion

The "no" campaign in 1988 argued that this change would undermine States' rights, i.e. that it would move - or make it possible to move - some power from State Governments to Local Governments.

There is a proposal to hold a further referendum

Referendum

A referendum is a direct vote in which an entire electorate is asked to either accept or reject a particular proposal. This may result in the adoption of a new constitution, a constitutional amendment, a law, the recall of an elected official or simply a specific government policy. It is a form of...

in 2011 on inclusion of Local Government in the Constitution of Australia.