The region's Police and Crime Panel, which is made up of councillors and members of the public, recently voted to allow an average £24 hike a year in council tax bills to fund extra numbers of frontline staff.
The increase had been proposed by West Yorkshire's Police and Crime Commissioner (PCC) Mark Burns-Williamson, who said he was "conscious" of the impact on hard-pressed families, but claimed it was a necessary move to make communities safer.
The Panel subsequently wrote to Policing Minister Nick Hurd to express concerns about the force being financed through local taxation, and the impact on the poorest people in the region. Members said they felt they had "no choice" but to approve the rise.
In response, Mr Hurd said it was right that the decision was taken at a local level, but added that he "understood" concerns raise about the long-term viability of police funding.
In her open letter to the government, Police and Crime Panel chair Councillor Alison Lowe said: "We feel the settlement was in fact a way of government putting yet more onus on the council tax payer to fund police officers.
"West Yorkshire has had to face significant government cuts of over £140 million since 2010 and over 2,000 police jobs have been lost in total. "
"Police services (are) facing a cliff edge in the year ahead unless it is properly addressed in the next Comprehensive Spending Review.
"In order to tackle crime effectively, we need a well-funded, well-trained and well-supported police force that is rooted in the communities it serves so that
crime is reduced and victims are supported.
"The impact of austerity, Brexit and the ongoing financial uncertainty has substantially impacted the people of West Yorkshire.
"The continued trend of replacing central funding with local taxation puts an added burden on the poorest in our communities and we ask for a review of this policy."
Mr Hurd's reply will be discussed at the Panel's next meeting this Friday.
He wrote: "I welcome your decision to approve the Police and Crime Commissioner's request...and have taken careful note of your reservations about the increase, including the impact on local tax payers.
"The government believes that an increase in council tax of £2 a month for an average Band D households is manageable, but it is right that these decisions are taken locally in consultation with the public.
"I understand your concerns about the longer term position beyond next year.
"Funding decisions for the medium term will be taken in the round as part of the next Spending Review.
"We have been working closely with the police to build a clear evidence base on future demand and financial pressures to help inform these decisions."