"The council is worried about that [request], because effectively we see that as a transfer of government responsibility on to local government," he said.
In an effort to see how big the problem was nationally, Mr Yule emailed on Friday every mayor in New Zealand. He said he wanted to find out what other local authorities were doing to "fill the gap".
In regards to Hastings District, the mayor said he was happy to support things like Neighbourhood Support, because that was about a community looking after itself.
He said in terms of core policing roles - ensuring health and safety, holding offenders to account on theft and burglaries, in addition to more serious crimes - it was not the role of councils, but rather "a government role".
Mr Yule, who is also president of Local Government NZ, wanted to make it clear that he was not "having a go" at the local police regime.
"What we are talking about is whether actually there are enough national resources being made [available] to policing," he said.
Police Minister Judith Collins said advances in technology had freed up more frontline police resources, and police wanted to take advantage of that by focusing efforts on the specific drivers of crime in each community.
"This is not about reducing service or staffing levels - it is about police re-organising to focus on preventing crime and crashes and being out there for communities, reducing the number of victims and making the public safer," she said. "An increased investment in technology for police's frontline staff have allowed them to be more visible and deliver over half a million additional frontline hours each year, or the equivalent of 354 extra officers."
Mr Yule said, following the Flaxmere request, Hastings council was visited by the local police about three weeks ago to explain what they were doing in the community.
"The council's view after that was actually we actually think based on the resources they are doing all they can," he said.
He said one of the issues raised was the policing budget, which, according to reports he had received, had been frozen for five years. He questioned whether it was that reported budget freeze that had seen the transfer of costs to ratepayers, when "those costs are actually a central government responsibility".
Ms Collins said it was "not correct" to say police budgets had been frozen. "For example, the Eastern district area has had a significant budget increase in recent years, from $51.9 million in 2010/11 to $55.2 million in 2015/16. Also last year in the 2015 Budget, the Government announced that police's operating spending was increasing by $41 million per annum to support their work."
The minister said the Government and police were always looking to ensure the public got the best possible value from its allocated budget and that local communities were provided with an effective policing service.
"Police districts run their own targeted activities based in response to particular issues in their communities, and prioritise and focus their resources accordingly based on the needs of their local area," Ms Collins said.
Mr Yule said one way of dealing with the issue was to give the local authorities more money to help deal with it. [But] I don't think that is our preference.
"I think our preference is to say look, this is a core responsibility of the Crown, we are not going to continue to pick up these costs. When a community doesn't feel safe or wants something done about petty crime, why is that a ratepayer issue? It's a central government issue." If enough support was given to Mr Yule on the issue, the council would table a remit at this year's Local Government New Zealand conference this July.
A police spokeswoman said the service "will not be commenting on budget issues".