Kirklees Council is considering the idea as it faces having to make cuts to its budget of around £70 million over the next three years.
As many as 1,000 of the authority’s 7,000 staff could also lose their jobs as the council contemplates drastic cuts covering everything it does from caring for adults and children to reductions in libraries and museums.
The Government has repeatedly capped council tax rises at two per cent and given financial incentives to those who freeze their bills.
Authorities have been told they can increase their bills by more if they secure public support in a local referendum.
So far, no council has taken that option because of the costs of holding the vote and the likelihood it will return a ‘no’ verdict.
Brighton Council came close to holding a referendum last year but it was scrapped as part of a last-minute budget deal.
Kirklees will test public opinion on the idea of a referendum which could allow the council to increase bills by five per cent as part of a much wider consultation on the unpalatable choices facing the authority.
Council leader David Sheard said: “I am asking the public, rather than having a costly referendum, let’s get feedback on whether there is the will for it or not.”
The referendum idea will included in early budget proposals considered by the council’s cabinet next week.
Earlier this year it emerged that Kirklees was considering retaining just two of its 26 libraries with the rest run by the community or closed.
Other measures also being considered include removing council subsidies for adult and children’s services except where they are required by law, cutting all council spending on police community support officers and asking the public to take more responsibility for maintaining parks and keeping streets clean.
The number of museums could be reduced to just two along with the Huddersfield Art Gallery while the open markets at Batley and Birstall could close.
Transport subsidies could be removed from faith and special schools and council funded events and concerts scrapped.
Coun Sheard said the council was starting the budget process early to give councillors, the public, unions and community groups the chance to have their say.
But he warned that simple opposition to cuts was not an option given the financial challenge facing the authority and preserving services would involve major changes to the way they are run.
While Kirklees has started its budget process early, councils across Yorkshire are expected to set out a similarly stark picture of their finances in the months ahead as they cope with falls in Government funding and increasing demands for services.
Local Government Minister Kris Hopkins yesterday visited Sheffield as part of a wider tour looking at areas where councils are working with other public bodies, such as the NHS, to improve services while cutting costs from duplication.
The former Bradford Council leader said the work of councils was “undervalued” and they had “responded tremendously” to the challenges they face.
But he warned that local authorities would not see a dramatic change in their finances after the next election.
“I want to see a Conservative majority but whichever government is in power is going to have to face up to the fact that there will not be a return to the mad years of the last Labour government where people were recklessly spending money.”
He said the Government had made £410 million available to help councils redesign services which “cannot go on as they were in individual silos”.
Mr Hopkins said co-ordinating services to get better value for money involved co-operation at all levels of organisations and that this was happening already in many places.
“The reality is reduced amounts of money going to local government is here to stay as in all public services for years to come.”